Monday 30 July 2012

latihan isotop

1 Karbon-14 adalah satu isotop karbon. Ia mempunyai 8 neutron.
              Lukis dan huraikan struktur atom bagi karbon-14.


2    Berikan satu contoh lain isotop karbon.
Nyatakan bilangan neutron dalam isotop itu.
Tuliskan symbol bagi isotop itu dalam bentuk  
A
         X
                 
Z

3    Apakah perbezaan  antara
jisim isotop d.engan jisim atom

Thursday 26 July 2012

sinar beta,gamma,alpha

1.     Jelaskan apa yang anda ketahui tentang proses terjadinya  sinar alfa, sinar beta, sinar gamma dan sinar X
2.     Jelaskan persamaan dan perbedaan
  1. sinar alfa dengan atom helium
  2. Sinar beta dengan elektron
  3. Sinar gama dengan sinar X
3.     Jelaskan bilamana suatu inti dikatakan stabil menurut konsep:
  1. perbandingan n/p
  2. energi ikat per nukleon
  3. inti ganjil-genap
4.     Gambarkan peta nuklida dan dan berikan penjelasan berkaitan dg ksabilan inti dan radionuklida
5.     238U92     1   234Th90      2   234Pa91      3     234U92    4      230Th92    
a)Partikel apa yang dipancarkan pd tiap peluruhan, b)berapa pasang isotop dan isobar
6.     Sebutkan deret radioaktif alam dan persamaannya, deret mana yang sudah tdk dikenal lagi, mengapa?
7.     Radionuklida Cl-38 (waktu paruh 37,38 menit) meluruh dengan memancarkan sinar beta dengan energi:
1,11 MeV sebanyak 31 %
2,77 MeV sebanyak 16 %
4,81 MeV sebanyak 53 %
dan memancarkan sinar gama dengan energi 1,50 MeV; 2,16 MeV dan 3,66 MeV.
     Gambar skema luruhnya !
8.     Suatu radionuklida meluruh sebagai berikut:
t (jam)                     0          2,5        5,0        7,5        10
aktivitas (dpm)        180       130       104       77         39
Tentukan besarnya waktu paruh dengan:
     (metode grafik)
9.     Berdasarkan besarnya energi ikat inti, ramalkan nuklida mana yang lebih stabil.
  1. C-12 atau C-13
  2. Li-6 atau Li-7
  3. N-14 atau N-15
Diketahui massa atom masing-masing nuklida (s.m.a) adalah:
                  C-12     = 12,0000          C-13     = 13,0075   
N-14     = 14,0077          N-15     = 15,0098
                  Li-6       = 6,0170           Li-7       = 7,0480
n = 1,008930 sma    p = 1,0081437 sma
10.  Larutan mengandung 1,5 mCi Au-198 per ml. Berapa aktivitas larutan 0,05 ml Au-198 pada 10 hari kemudian. Diketahui waktu paruh Au-198 adalah 65 jam.
11.  Berapa persen cuplikan Co-60 yang tinggal setelah 4 tahun. Waktu paruh Co-60 = 5,26 tahun

radioaktif

latihan radioaktif

latihan radioaktif

Lengkapkan persamaan berikut:

Tuesday 24 July 2012

pembelajaran kooperatif


STRATEGI KOPERATIF DAN KOLABORATIF

Secara umum, strategi koperatif dan kolaboratif memerlukan pelajar bekerjasama dalam kumpulan bagi mengatasi sesuatu masalah, memberi maklum balas dan berkomunikasi serta berinteraksi antara satu sama lain secara berstruktur.

Pembelajaran Koperatif (PK)


Banyak pendekatan pembelajaran koperatif diperkenalkan oleh beberapa tokoh terkenal seperti Kagan, Johnson & Johnson, Cooper, Graves & Graves, Millis dan Slavin. Modul ini memilih pembelajaran koperatif yang diperkenalkan oleh  Kagan (1988) untuk digunakan sebagai pendekatan utama. Walau bagaimana pun, pendekatan-pendekatan oleh tokoh-tokoh yang lain juga boleh diperkenalkan. Untuk tujuan kursus, modul ini melaksanakan cadangan pendekatan pelaksanaan strategi pembelajaran seperti yang ditunjukkan dalam Rajah  di bawah.





Rajah  : Cadangan Pelaksanaan Kursus Pembelajaran Koperatif (PK)

           

Definisi dan konsep


Pembelajaran Koperatif didefinisikan sebagai satu set proses yang membantu pelajar berinteraksi satu sama lain untuk mecapai satu matlamat khusus atau mendapatkan satu hasil akhir (end-product) yang  ada kaitan dengan isi kandungan mata pelajaran. Pendekatan berstruktur (structural approach) dalam pembelajaran koperatif oleh Kagan hasil daripada proses mencipta, menganalisis dan mengaplikasikan struktur (yang tidak terikat kepada isi kandungan pelajaran) secara sistematik termasuk cara-cara menguruskan interaksi sosial dalam bilik darjah.

Menurut Kagan (1998), dalam pembelajaran koperatif, aktiviti pembelajaran dikatakan wujud apabila struktur koperatif  yang disesuaikan dengan isi kandungan seperti yang diwakili oleh hubungan di bawah.
 

Struktur pembelajaran  +  Isi kandungan  =  Aktiviti.


Kagan telah menyenaraikan sekurang-kurangnya sebanyak lebih daripada 50 contoh struktur (dengan nama-nama yang tertentu)   yang dapat  disesuaikan dengan isi kandungan.

Struktur boleh digunakan mengikut tujuan tertentu – team building (kumpulan kecil), Classbuilding (satu kelas), Masteri, Kemahiran berfikir, Perkongsian Maklumat dan Kemahiran berkomunikasi.

Contoh dalam Rajah  di bawah menunjukkan bagaimana aktiviti dibentuk apabila struktur Roundtable digabungkan dengan isi kandungan (satu senarai nombor perdana atau contoh lain seperti haiwan jinak, kata adjektif)












Struktur-struktur koperatif boleh digabungkan dengan isi kandungan yang sesuai pada setiap peringkat pengajaran (set induksi, langkah perkembangan, penutup dan latihan).


Ciri-ciri utama pembelajaran koperatif.

Banyak kajian mendapati pembelajaran koperatif mempunyai banyak kelebihan, antaranya ialah dapat meningkatkan potensi pelajar dari segi
  • Pencapaian akademik
  • Kepekaan positif kepada kepelbagaian
  • Pemantapan kemahiran sosial

Pembelajaran Koperatif menggunakan peraturan bilik darjah yang mampu mewujudkan satu pasukan yang berkesan. Singkatan KISSES mewakili peraturan bilik darjah seperti yang diterangkan di bawah.

K         Keep with the group (Sentiasa dalam pasukan)
I           Include everyone  (libatkan semua ahli – elakkan passenger)
S          Share ideas and feelings (sedia berkongsi idea dan perasaan)
S          Stay on task (Sentiasa melakukan tugasan yang diberi)
E          Encourage others (Memberi galakan kepada rakan sebaya)
S          Six inch Voices ( perbincangan mesra kumpulan berberdua /
            berempat dalam  jarak  lebih kurang 6 inci.)

Konsep Utama Dalam Pembelajaran Koperatif


Terdapat  enam konsep utama dalam proses pembelajaran koperatif. Konsep ini merangkumi

  • Pasukan – ada visi, berstruktur untuk perkembangan minda positif,
  • Kemahiran sosial
  • Pengurusan (termasuk isyarat senyap)
  • Prinsip PIES
  • Keazaman / kemahuan (willingness) untuk bekerjasama
  • Struktur-struktur (Kagan)


Prinsip PIES (salah satu konsep pembelajaran koperatif) ialah

  • P  Pergantungan positif (Positif interdependence)
  • I   Akauntabiliti individu (Individual accountabilitiy)
  • E  Penglibatan seimbang/sama (Equal participation)
  • S  Interaksi serentak (Simultaneous interaction)

Mengikut Kagan, tidak semua aktiviti berkumpulan boleh digolongkan sebagai pembelajaran koperatif melainkan struktur yang digunakan memenuhi keempat-empat prinsip yang tersebut di atas.

Suasana pembelajaran yang kondusif dapat diwujudkan melalui pembelajaran koperatif melalui

  • Bilik darjah yang demokratik
  • Memberi ‘Empowerment ‘ kepada pelajar
  • Peranan guru sebagai fasilitator dan mentor


Ciri-ciri Pembelajaran Koperatif
Terdapat pelbagai pendapat mengenai ciri-ciri pembelajaran koperatif.
Slavin (1990) berpendapat, pembelajaran koperatif hanya berkesan apabila ia mempunyai tiga ciri berikut: ganjaran kumpulan, tanggungjawab individu dan peluang yang sama untuk berjaya.  
Johnson & Johnson (1994) pula menggariskan lima ciri pembelajaran koperatif. Ciri-ciri tersebut adalah matlamat kumpulan, peranan ahli, interaksi, kemahiran berkumpulan dan penilaian kumpulan.
Ganjaran kumpulan:
Pelajar akan diberikan ganjaran apabila kumpulan mereka mencapai sesuatu kriteria tertentu tanpa ada sebarang persaingan antara sesama kumpulan. Ganjaran kumpulan menjadikan pelajar lebih bermotivasi untuk melibatkan diri dalam aktiviti berkumpulan.
Tanggungjawab individu:
Tanggungjawab individu bermaksud semua ahli kumpulan bertanggungjawab menentukan kejayaan sesuatu kumpulan. Ini akan mendorong pelajar membimbing rakan-rakan sekumpulan dan semua ahli bertanggungjawab menguasai pelajaran.
Peluang yang sama untuk berjaya:
Ia merujuk kepada pencapaian pelajar diukur berdasarkan peningkatan prestasi masing-masing. Oleh itu, semua pelajar berpeluang meningkatkan pencapaian kumpulan mereka tanpa mengira tahap kebolehan masing-masing.
Matlamat kumpulan:
Pelajar mesti bekerjasama dalam satu kumpulan untuk mencapai matlamat yang telah ditetapkan. Tanpa kerjasama antara ahli, sesuatu kumpulan tidak dapat mencapai matlamat tersebut.

Peranan ahli:
Ia merujuk kepada tanggungjawab individu dan kumpulan, iaitu sesebuah kumpulan bertanggungjawab mencapai matlamatnya dan setiap individu bertanggungjawab memberi sumbangan kerja yang sepatutnya.
Interaksi:
Pembelajaran koperatif seharusnya menggalakkan interaksi, sebaik-baiknya secara bersemuka. Pelajar melakukan kerja secara bersama melalui perkongsian bahan, saling tolong-menolong dan memberi galakan antara satu sama lain.
Kemahiran berkumpulan:
Pelajar perlu disediakan dengan kemahiran bersosial dan kemahiran untuk bekerja secara berkumpulan. Kedua-dua kemahiran ini perlu bagi membolehkan sesebuah kumpulan berfungsi dengan baik. Contohnya, kemahiran menguruskan sebarang konflik yang timbul di dalam kumpulan.
Penilaian kumpulan:
Dalam penilaian kumpulan, ahli kumpulan berbincang dan menganalisis setakat mana kumpulan mereka mencapai matlamat yang dikehendaki. Pelajar mengenal pasti tindakan dan tingkah laku yang perlu diperbaiki atau dihentikan.
Prinsip-prinsip Pembelajaran Koperatif
Dalam menerangkan prinsip-prinsip pembelajaran koperatif, terdapat dua model yang boleh dijadikan rujukan. Model-model tersebut adalah model yang dihasilkan oleh Johnson & Johnson dan model Kagan. Topik ini akan menfokuskan kepada prinsip-prinsip pembelajaran koperatif mengikut model Kagan.
PIES merupakan prinsip-prinsip pembelajaran koperatif mengikut model Kagan. Apakah PIES? Klik pada setiap huruf di bawah untuk penerangan lanjut.


Positive Interdepence (Saling Kebergantungan Secara Positif):
Pembelajaran koperatif merujuk kepada kaedah pengajaran yang memerlukan pelajar dari pelbagai kebolehan bekerjasama dalam kumpulan kecil untuk mencapai satu matlamat yang sama. Sasaran adalah tahap pembelajaran yang maksimum bukan sahaja untuk diri sendiri, tetapi juga untuk rakan-rakan yang lain. Saling bergantungan secara positif yang kuat di dalam sesuatu kumpulan akan menjadi motivasi kepada setiap ahli untuk berjaya.

Individual Accountability (Akauntabiliti Individu):
Bagi menilai akauntabiliti individu setiap ahli kumpulan, satu tugasan akan diberikan kepada kumpulan tersebut. Pencapaian kumpulan akan dinilai mengikut sumbangan setiap individu. Setiap ahli akan menerima markah mengikut sumbangan / idea mereka.
Equal Participation (Penglibatan Sama Rata):
Penglibatan yang sama rata di antara ahli kumpulan boleh dicapai melalui pembahagian/urutan tugasan. Dengan cara ini, setiap pelajar diberi peluang untuk mengambil bahagian dan memberi idea. Cara ini menjadikan setiap pelajar bertanggungjawab dan menglibatkan mereka secara sama rata.
Structure (Struktur):
Terdapat banyak struktur dalam model Kagan dimana setiap satunya mempunyai kegunaan dan kepentingan masing-masing. Pengetahuan mengenai struktur-struktur ini dan cara pelaksanaanya memerlukan pemahaman dan latihan yang berulang-ulangan. Anda akan mempelajari mengenai struktur-struktur ini dalam mukasurat seterusnya.
Model Johnson & Johnson menggariskan 4 prinsip pembelajaran koperatif:

1. Positive Interdependence (Saling Kebergantungan Secara Positif)
Pelajar seharusnya beranjak dari sifat bergantung kepada sifat berdikari dan seterusnya ke tahap saling kebergantungan. Saling kebergantungan wujud apabila pelajar menganggap bahawa ia memerlukan usaha orang lain untuk menyelesaikan sesuatu tugasan. Walaupun seseorang pelajar berdikari tetapi tahap kecemerlangan yang lebih tinggi cuma boleh dicapai melalui usaha, input dan sinergi orang lain.

2. Individual Accountability (Akauntabiliti Individu)
Walaupun setiap pelajar dikehendaki bekerjasama dalam sesuatu tugasan, ia adalah bertanggungjawab atas pencapaiannya sendiri. Penilaian boleh dibuat secara individu.

3. Group Interaction (Interaksi Kumpulan)
Pelajar-pelajar memajukaan pembelajaran pelajar lain dengan membantu, mengkongsi dan menggalakkan usaha pembelajaran. Interaksi kumpulan termasuk tindakan pelajar untuk menerangkan, membincang dan mengajar apa yang diketahui kepada orang lain.


4. Social Skills (Kemahiran Sosial)
Agar pembelajaran koperatif berkesan, guru mesti mengajar kemahiran sosial kepada pelajar. Kemahiran-kemahiran tersebut merangkumi kepimpinan, membuat keputusan, membina kepercayaan, komunikasi dan pengurusan konflik.
Struktur-struktur Pembelajaran Koperatif
Setiap prinsip dalam pembelajaran koperatif model Kagan boleh dicapai menerusi salah satu dari kemahiran-kemahiran di bawah:
1.  Think-Pair-Share

Pelajar akan diberi satu soalan dan diberi masa untuk memikirkan jawapannya
secara bersendirian untuk jangkamasa tertentu. Kemudian, secara berpasangan,
mereka akan membandingkan jawapan-jawapan mereka dan
mempersembahkannya di dalam kelas.

2. Round Robin

Di dalam struktur ini, setiap pelajar memberikan idea setiap kali sampai giliran
mereka.

3. Persemukaan (Trade a Problem)

Di dalam struktur ini, setiap pasukan memerlukan satu set soalan yang ditulis
pada kad. Sebelah depan kad yang mengandungi soalan dilabelkan sebagai “S”
dan bahagian belakang kad yang mengandungi jawapan dilabelkan sebagai “J”.
Ahli kumpulan A akan menayangkan “J” apabila tiada jawapan tepat yang
diterima dari kumpulan B.

4. Pembahagian tugas (Assigning Roles)
Di dalam struktur ini, setiap ahli diberikan peranan masing-masing, contohnya,
pencatat idea, memanjangkan idea kumpulan kepada kumpulan lain dan
sebagainya.

 Konsep dan Prinsip dalam Pembelajaran Koperatif

Pengintegrasian pembelajaran koperatif dalam pengajaran dan pembelajaran dapat dilakukan melalui proses perancangan, pengendalian, pengurusan dan penilaian yang ditunjukkan dalam Rajah  di bawah.






Ringkasnya, pembelajaran koperatif mengganggap kejayaan insan bukan tertakluk kepada kecemerlangan  akademik semata-mata. Perkembangan kecerdasan intelektual(IQ), sosial dan afektif (EQ) merupakan teras bagi pembelajaran koperatif melalui amalan interaksi kumpulan yang berkesan. Pembelajaran koperatif menyediakan gelanggang bagi pelajar mengalami dan membina realiti hidup dalam era sains dan teknologi yang pesat berkembang. Di samping membentuk ‘independent thinkers’, pembelajaran koperatif juga berusaha ke arah membentuk kemahiran berinteraksi, hormat-menghormati dan berkomunikasi secara positif dalam masyarakat

Berasaskan kepada ‘brain-based learning’gaya pembelajaran dan kecerdasan pelbagai, pembelajaran koperatif menganggap bahawa setiap individu mempunyai potensi untuk berjaya. Kejayaan adalah tanggungjawab bersama antara individu, rakan sebaya dan unsur-unsur dalam persekitarannya. 


Secara amnya, cadangan prosedur pelaksanaan bagi setiap struktur koperatif yang dinyatakan di atas akan melalui proses seperti yang ditunjukkan dalam Rajah  di bawah.





















Masa untuk mengendalikan sesuatu struktur adalah fleksibel. Adalah diharapkan peserta dapat didedahkan dengan seberapa banyak struktur yang dapat sesuai dengan mata pelajaran masing-masing. Untuk meningkatkan kemahiran ini, peserta diharap dapat belajar secara terarah kendiri.



 PEMBELAJARAN KOLABORATIF


Strategi pembelajaran kolaboratif merupakan salah satu strategi yang boleh digunakan dalam pengajaran dan pembelajaran bestari. Walaupun ada persamaan dalam beberapa aspek tetapi pembelajaran kolaboratif berbeza daripada pembelajaran koperatif. Pembelajaran kolaboratif mempunyai ciri-ciri utama, antaranya, seperti berikut;

  • Perkongsian maklumat antara guru dan murid atau murid dan murid – cth maklumat hasil carian internet dikongsi bersama.
  • Perkongsian kuasa antara guru dan murid – empowermentkepada murid menentukan objektif sesuatu tugasan setelah dipersetujui oleh guru, menggunakan kreativiti mereka menyiapkan tugasan seperti menggunakan pengurusan grafik  dll.
  • Guru sebagai mediators – bantu murid mengaitkan maklumat baru yang diperolehi dari usaha kolaboratif dengan pengalaman dan pemindahan kepada situasi baru.
  • Kewujudan personaliti dan harga diri positif hasil perkongsian maklumat sesama rakan sebaya dan guru.

Perbezaan di antara pembelajaran koperatif dan pembelajaran kolaboratif ditunjukan dalam jadual di bawah.



Pembelajaran Koperatif
Pembelajaran Kolaboratif
Satu strategi pembelajaran berteraskan pasukan kecil. Setiap murid bertanggungjawab tentang pencapaian diri sendiri dan membantu ahli kumpulan

Berasaskan kepada idea bahawa pembelajaran adalah satu tingkah laku sosial. Pembelajaran berlaku melalui perbincangan atau komunikasi fizikal atau virtual.
Pergantungan positif setiap ahli dalam menentukan kejayaan pasukan.
Tiada ‘kontrak’ / pergantungan dalam kolaborasi bersama.
Peranan guru sebagai fasilitator, menstrukturkan dan  memantau aktiviti pasukan mencapai objektif.
Tidak memerlukan pemantauan guru dan tidak berstruktur.

Hasil secara kumpulan
Hasil secara individu.


Lawat laman web berikuthttp://www.ncbe.gwu.edu/ncbepubs/directions/12.htm -

What Is the Collaborative Classroom? untuk mendapatkan keterangan lanjut.

Bibiliografi Pembelajaran Koperatif dan Kolaboratif

1.    Dewey, J. (1916). Democracy and Education, New York: Macmillan

2.    Johnson, D. W., and Johnson, F.P. (1994). Joining Together : Group Theory and Group Skills (4th ed.). Englewood Cliffs, N.J.: Prentice Hall.\

3.    Laura K. (1997). Discovering Decimal Through Cooperative Learning.

4.    Spencer Kagan (1988). Coperative Learning: Resources for Teachers.


Laman Web Yang berkaitan


1.         http://college.hmco.com/education/pbl/tc/coop.html

2.         http://www.winona.edu/fdc/_TheWell/00000001.htm

3.         http://volcano.und.nodak.edu/vwdocs/msh/llc/is/cl.html

4.         http://chiron.valdosta.edu/whuitt/col/instruct/cooplrn.html

5.         http://www.cde.ca.gov/iasa/cooplrng2.html

6.         http://www.ed.gov/databases/ERIC_Digests/ed422586.html

7.         http://chd.gse.gmu.edu/immersion/knowledgebase/strategies/constructivism
             /collaborative.htm
8.             http://www.ncbe.gwu.edu/ncbepubs/directions/12.htm
9.         http://teaching.berkeley.edu/bgd/collaborative.html

konstruktivisme


KONSTRUKTIVISME


Apa yang dimaksudkan dengan konstruktivisme?

Konstruktivisme adalah suatu proses pembelajaran yang menerangkan bagaimana pengetahuan disusun dalam minda seseorang murid. Konstruktivisme juga merupakan satu kepercayaan  bahawa pembelajaran bermula daripada pengetahuan dan pengalaman yang tersimpan dalam storan memori atau struktur kognitif murid.

Ilmu pengetahuan sebenarnya tidaklah boleh dipindahkan daripada guru kepada murid seperti memindahkan barang dari satu bekas kebekas yang lain. Seseorang murid itu perlu membina sesuatu pengetahuan itu mengikut pengalaman masing-masing. Pembelajaran berlaku daripada hasil usaha murid itu sendiri dan tidak mungkin berlaku dimana seseorang guru itu boleh belajar untuk muridnya. Fikiran murid tidak akan menghadapi realiti yang wujud secara terasing dalam persekitaran tetapi realiti yang diketahui oleh murid adalah realiti yang dia bina sendiri. Sesungguhnya murid telah pun mempunyai satu set idea dan pengalaman yang membentuk struktur kognitif terhadap persekitaran mereka.

Dalam proses membantu murid membina atau menerima sesuatu idea atau konsep baru, guru perlulah mengambil kira struktur kognitif yang sedia ada pada mereka atau apa yang dikatakan sebagai pengetahuan sedia ada murid. Apabila maklumat baru telah dapat disesuaikan dan diterima untuk dijadikan pegangan kuat mereka, barulah suatu kerangka baru tentang sesuatu Iimu Pengetahuan itu dapat dibina. Proses inilah yang dinamakan sebagai Konstruktivisme.

Rutherford dan Ahlgren berpendapat bahawa murid mempunyai idea mereka sendiri tentang hampir semua pekara, di mana ada yang betul dan ada yang salah. Jika kefahaman dan miskonsepsi ini dibiarkan atau tidak diperbetulkan dengan baik, kefahaman dan pegangan asal mereka itu akan tetap kekal.

John Dewey menguatkan lagi teori konstruktivisme ini dengan mengatakan bahawa pendidik yang cekap harus melaksanakan pengajaran dan pembelajaran sebagai proses menyusun atau membina pengalaman secara berterusan. Beliau juga menekankan kepentingan penyertaan murid di dalam setiap aktiviti pengajaran dan pembelajaran.

Apakah peranan guru dalam pengajaran dan pembelajaran yang berasaskan Pendekatan Konstruktivisme?

Dari perspektif epistemologi yang disarankan dalam konstruktivisme peranan guru akan berubah. Perubahan akan berlaku dalam teknik pengajaran dan pembelajaran, penilaian, penyelidikan dan cara melaksanakan kurikulum. Perspektif ini akan mengubah kaedah pengajaran dan pembelajaran yang menumpu kepada kebolehan murid meniru dengan tepat apa yang disampaikan oleh guru kepada kaedah pengajaran dan pembelajaran yang menumpukan kepada kebolehan murid membina konsep berdasarkan kepada pengalaman yang aktif. Ia juga akan mengubah tumpuan penyelidikan daripada pembinaan model daripada kaca mata guru kepada pembinaan idea atau konsep daripada pengalaman murid. Perubahan juga dapat dilihat daripada pengajaran secara deduktif kepada pengajaran secara induktif.

Pengajaran dan pembelajaran yang berasaskan konstruktivisme mementingkan guru dan murid memainkan peranan yang saling bersandar diantara satu sama lain.



             PERANAN  GURU                                    PERANAN  MURID
 

1. Guru tidak menganggap bahawa minda     Murid   tidak  mengangap     guru      sebagai           
    murid adalah seperti tin kosong yang         pembekal  maklumat  tetapi  sebagai   salah     
    perlu diisikan dengan fakta dan pengeta    satu sumber pengetahuan untuk membantu 
    -huan baru.                                                  mereka mencari maklumat  dan menggalak-
                                                                       -kan mereka berfikir dan berkomunikasi.

2. Guru berperanan sebagai seorang              Murid  bertanggungjawab terhadap  segala
    fasilitator dan pembimbing.                       usaha  untuk mencari   pelbagai cara untuk
                                                                       memproses   maklumat dan  menyelesaikan
                                                                       masalah.

3. Guru berperanan sebagai pengurus bilik   Murid  berdisiplin  dalam membuat keputu
    darjah untuk menangani hal-hal disiplin   -san  sendiri untuk  melibatkan   diri  dalam 
    murid dengan sempurna.                           aktiviti  pembelajaran.     


Apakah ciri-ciri guru konstruktivisme?

Diantara ciri-ciri guru konstruktivisme adalah seperti berikut:
1. sentiasa memberi galakan dan boleh menerima pandangan, pendapat serta inisiatif pelajar.
2.  menggunakan data dan maklumat asal yang belum diproses serta menggunakan bahan-bahan yang membawa kearah kemahiran manipulatif, interaktif dan kemahiran fizikal.
3. dalam membuat rangka kerja, biasanya menggunakan terminologi kognitif seperti pengkelasan, analisis, meramal dan merekacipta.
4. memberi peluang kepada pelajarnya berinteraksi untuk menghidupkan suasana pengajaran dan pembelajaran, menukar arahan dalam strategi dan mengubahsuai isi pelajaran.
5. mengenalpasti kefahaman murid terhadap sesuatu konsep terlebih dahulu sebelum kefahamannya dikongsikan. 

6.  menggalakkan pelajar-pelajarnya untuk berdialog , samaada dengan guru atau sesama mereka.
7.  menggalakkan penggunaan kaedah inkuari dikalangan pelajar dengan mengemukakan soalan yang menekankan kemahiran berfikir, “open-ended questions” dan menggalakkan pelajar untuk mengemukakan soalan sesama sendiri.
8.  melihat dan mengambil kira perkembangan respon pelajar diperingkat awal.
9. mengikat pelajar melalui pengalaman yang  mungkin tidak sama dengan hipotesis asalnya dan ini akan menimbulkan perbincangan.
10. memberi masa yang cukup selepas sesuatu soalan dikemukakan.
11. memperuntukkan masa yang sesuai untuk pelajar membina hubungan dan mewujudkan “metaphors”.
12. melatih keinginan semulajadi pelajar melalui kekerapan penggunaan model kitaran pembelajaran.  

Apakah strategi yang perlu digunakan?

Strategi yang perlu digunakan oleh seorang guru yang mengamalkan pendekatan konstruktivisme dalam pengajarannya bolehlah dirujuk kepada peta konsep dibawah.


Thursday 19 July 2012

SAINS 2 PHOTON


Photon

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Photon
Military laser experiment.jpg
Photons emitted in a coherent beam from a laser
Composition Elementary particle
Statistics Bosonic
Interactions Electromagnetic
Symbol γ, hν, or ħω
Theorized Albert Einstein
Mass 0
<1×10−18 eV/c2[1]
Mean lifetime Stable[1]
Electric charge 0
<1×10−35 e[1]
Spin 1
Parity −1[1]
C parity −1[1]
Condensed I(JPC)=0,1(1−−)[1]
A photon is an elementary particle, the quantum of light and all other forms of electromagnetic radiation, and the force carrier for the electromagnetic force, even when static via virtual photons. The effects of this force are easily observable at both the microscopic and macroscopic level, because the photon has no rest mass; this allows for interactions at long distances. Like all elementary particles, photons are currently best explained by quantum mechanics and exhibit wave–particle duality, exhibiting properties of both waves and particles. For example, a single photon may be refracted by a lens or exhibit wave interference with itself, but also act as a particle giving a definite result when its position is measured.
The modern concept of the photon was developed gradually by Albert Einstein to explain experimental observations that did not fit the classical wave model of light. In particular, the photon model accounted for the frequency dependence of light's energy, and explained the ability of matter and radiation to be in thermal equilibrium. It also accounted for anomalous observations, including the properties of black body radiation, that other physicists, most notably Max Planck, had sought to explain using semiclassical models, in which light is still described by Maxwell's equations, but the material objects that emit and absorb light, do so in amounts of energy that are quantized (i.e., they change energy only by certain particular discrete amounts and cannot change energy in any arbitrary way). Although these semiclassical models contributed to the development of quantum mechanics, many further experiments[2][3] starting with Compton scattering of single photons by electrons, first observed in 1923, validated Einstein's hypothesis that light itself is quantized. In 1926 the chemist Gilbert N. Lewis coined the name photon for these particles, and after 1927, when Arthur H. Compton won the Nobel Prize for his scattering studies, most scientists accepted the validity that quanta of light have an independent existence, and Lewis' term photon for light quanta was accepted.
In the Standard Model of particle physics, photons are described as a necessary consequence of physical laws having a certain symmetry at every point in spacetime. The intrinsic properties of photons, such as charge, mass and spin, are determined by the properties of this gauge symmetry. The photon concept has led to momentous advances in experimental and theoretical physics, such as lasers, Bose–Einstein condensation, quantum field theory, and the probabilistic interpretation of quantum mechanics. It has been applied to photochemistry, high-resolution microscopy, and measurements of molecular distances. Recently, photons have been studied as elements of quantum computers and for sophisticated applications in optical communication such as quantum cryptography.

Contents

Nomenclature

In 1900, Max Planck was working on black-body radiation and suggested that the energy in electromagnetic waves could only be released in "packets" of energy. In his 1901 article [4] in Annalen der Physik he called these packets "energy elements". The word quanta (singular quantum) was used even before 1900 to mean particles or amounts of different quantities, including electricity. Later, in 1905 Albert Einstein went further by suggesting that electromagnetic waves could only exist in these discrete wave-packets.[5] He called such a wave-packet the light quantum (German: das Lichtquant). The name photon derives from the Greek word for light, φῶς (transliterated phôs), and was coined[Note 1] in 1926 by the physical chemist Gilbert Lewis, who published a speculative theory in which photons were "uncreatable and indestructible".[6] Although Lewis' theory was never accepted as it was contradicted by many experiments, his new name, photon, was adopted immediately by most physicists. Isaac Asimov credits Arthur Compton with defining quanta of energy as photons in 1923.[7][8]
In physics, a photon is usually denoted by the symbol γ (the Greek letter gamma). This symbol for the photon probably derives from gamma rays, which were discovered in 1900 by Paul Villard,[9][10] named by Ernest Rutherford in 1903, and shown to be a form of electromagnetic radiation in 1914 by Rutherford and Edward Andrade.[11] In chemistry and optical engineering, photons are usually symbolized by , the energy of a photon, where h is Planck's constant and the Greek letter ν (nu) is the photon's frequency. Much less commonly, the photon can be symbolized by hf, where its frequency is denoted by f.

Physical properties

The photon is massless,[Note 2] has no electric charge,[12] and is stable. A photon has two possible polarization states and is described by exactly three continuous parameters: the components of its wave vector, which determine its wavelength λ and its direction of propagation. The photon is the gauge boson for electromagnetism,[13] and therefore all other quantum numbers of the photon (such as lepton number, baryon number, and flavour quantum numbers) are zero.[14]
Photons are emitted in many natural processes. For example, when a charge is accelerated it emits synchrotron radiation. During a molecular, atomic or nuclear transition to a lower energy level, photons of various energy will be emitted, from infrared light to gamma rays. A photon can also be emitted when a particle and its corresponding antiparticle are annihilated (for example, electron-positron annihilation).
In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p. This derives from the following relativistic relation, with m = 0:[15]
E^{2}=p^{2} c^{2} + m^{2} c^{4}.
The energy and momentum of a photon depend only on its frequency (ν) or inversely, its wavelength (λ):
E=\hbar\omega=h\nu=\frac{hc}{\lambda}
\boldsymbol{p}=\hbar\boldsymbol{k},
where k is the wave vector (where the wave number k = |k| = 2π/λ), ω = 2πν is the angular frequency, and ħ = h/2π is the reduced Planck constant.[16]
Since p points in the direction of the photon's propagation, the magnitude of the momentum is
p=\hbar k=\frac{h\nu}{c}=\frac{h}{\lambda}.
The photon also carries spin angular momentum that does not depend on its frequency.[17] The magnitude of its spin is \scriptstyle{\sqrt{2} \hbar} and the component measured along its direction of motion, its helicity, must be ±ħ. These two possible helicities, called right-handed and left-handed, correspond to the two possible circular polarization states of the photon.[18]
To illustrate the significance of these formulae, the annihilation of a particle with its antiparticle in free space must result in the creation of at least two photons for the following reason. In the center of mass frame, the colliding antiparticles have no net momentum, whereas a single photon always has momentum (since it is determined, as we have seen, only by the photon's frequency or wavelength—which cannot be zero). Hence, conservation of momentum (or equivalently, translational invariance) requires that at least two photons are created, with zero net momentum. (However, it is possible if the system interacts with another particle or field for annihilation to produce one photon, as when a positron annihilates with a bound atomic electron, it is possible for only one photon to be emitted, as the nuclear Coulomb field breaks translational symmetry.) The energy of the two photons, or, equivalently, their frequency, may be determined from conservation of four-momentum. Seen another way, the photon can be considered as its own antiparticle. The reverse process, pair production, is the dominant mechanism by which high-energy photons such as gamma rays lose energy while passing through matter.[19] That process is the reverse of "annihilation to one photon" allowed in the electric field of an atomic nucleus.
The classical formulae for the energy and momentum of electromagnetic radiation can be re-expressed in terms of photon events. For example, the pressure of electromagnetic radiation on an object derives from the transfer of photon momentum per unit time and unit area to that object, since pressure is force per unit area and force is the change in momentum per unit time.[20]

Experimental checks on photon mass

The photon is currently understood to be strictly massless, but this is an experimental question. If the photon is not a strictly massless particle, it would not move at the exact speed of light in vacuum, c. Its speed would be lower and depend on its frequency. Relativity would be unaffected by this; the so-called speed of light, c, would then not be the actual speed at which light moves, but a constant of nature which is the maximum speed that any object could theoretically attain in space-time.[21] Thus, it would still be the speed of space-time ripples (gravitational waves and gravitons), but it would not be the speed of photons.
A massive photon would have other effects as well. Coulomb's law would be modified and the electromagnetic field would have an extra physical degree of freedom. These effects yield more sensitive experimental probes of the photon mass than the frequency dependence of the speed of light. If Coulomb's law is not exactly valid, then that would cause the presence of an electric field inside a hollow conductor when it is subjected to an external electric field. This thus allows one to test Coulomb's law to very high precision.[22] A null result of such an experiment has set a limit of m ≲ 10−14 eV/c2.[23]
Sharper upper limits have been obtained in experiments designed to detect effects caused by the galactic vector potential. Although the galactic vector potential is very large because the galactic magnetic field exists on very long length scales, only the magnetic field is observable if the photon is massless. In case of a massive photon, the mass term \scriptstyle\frac{1}{2} m^2 A_{\mu}A^{\mu} would affect the galactic plasma. The fact that no such effects are seen implies an upper bound on the photon mass of m < 3×10−27 eV/c2.[24] The galactic vector potential can also be probed directly by measuring the torque exerted on a magnetized ring.[25] Such methods were used to obtain the sharper upper limit of 10−18eV/c2 (the equivalent of 1.07×10−27 atomic mass units) given by the Particle Data Group.[26]
These sharp limits from the non-observation of the effects caused by the galactic vector potential have been shown to be model dependent.[27] If the photon mass is generated via the Higgs mechanism then the upper limit of m≲10−14 eV/c2 from the test of Coulomb's law is valid.
Photons inside superconductors do develop a nonzero effective rest mass; as a result, electromagnetic forces become short-range inside superconductors.

Historical development

Thomas Young's double-slit experiment in 1805 showed that light can act as a wave, helping to defeat early particle theories of light.
In most theories up to the eighteenth century, light was pictured as being made up of particles. Since particle models cannot easily account for the refraction, diffraction and birefringence of light, wave theories of light were proposed by René Descartes (1637),[28] Robert Hooke (1665),[29] and Christian Huygens (1678);[30] however, particle models remained dominant, chiefly due to the influence of Isaac Newton.[31] In the early nineteenth century, Thomas Young and August Fresnel clearly demonstrated the interference and diffraction of light and by 1850 wave models were generally accepted.[32] In 1865, James Clerk Maxwell's prediction[33] that light was an electromagnetic wave—which was confirmed experimentally in 1888 by Heinrich Hertz's detection of radio waves[34]—seemed to be the final blow to particle models of light.
In 1900, Maxwell's theoretical model of light as oscillating electric and magnetic fields seemed complete. However, several observations could not be explained by any wave model of electromagnetic radiation, leading to the idea that light-energy was packaged into quanta described by E=hν. Later experiments showed that these light-quanta also carry momentum and, thus, can be considered particles: the photon concept was born, leading to a deeper understanding of the electric and magnetic fields themselves.
The Maxwell wave theory, however, does not account for all properties of light. The Maxwell theory predicts that the energy of a light wave depends only on its intensity, not on its frequency; nevertheless, several independent types of experiments show that the energy imparted by light to atoms depends only on the light's frequency, not on its intensity. For example, some chemical reactions are provoked only by light of frequency higher than a certain threshold; light of frequency lower than the threshold, no matter how intense, does not initiate the reaction. Similarly, electrons can be ejected from a metal plate by shining light of sufficiently high frequency on it (the photoelectric effect); the energy of the ejected electron is related only to the light's frequency, not to its intensity.[35][Note 3]
At the same time, investigations of blackbody radiation carried out over four decades (1860–1900) by various researchers[36] culminated in Max Planck's hypothesis[4][37] that the energy of any system that absorbs or emits electromagnetic radiation of frequency ν is an integer multiple of an energy quantum E=hν. As shown by Albert Einstein,[5][38] some form of energy quantization must be assumed to account for the thermal equilibrium observed between matter and electromagnetic radiation; for this explanation of the photoelectric effect, Einstein received the 1921 Nobel Prize in physics.[39]
Since the Maxwell theory of light allows for all possible energies of electromagnetic radiation, most physicists assumed initially that the energy quantization resulted from some unknown constraint on the matter that absorbs or emits the radiation. In 1905, Einstein was the first to propose that energy quantization was a property of electromagnetic radiation itself.[5] Although he accepted the validity of Maxwell's theory, Einstein pointed out that many anomalous experiments could be explained if the energy of a Maxwellian light wave were localized into point-like quanta that move independently of one another, even if the wave itself is spread continuously over space.[5] In 1909[38] and 1916,[40] Einstein showed that, if Planck's law of black-body radiation is accepted, the energy quanta must also carry momentum p=h/λ, making them full-fledged particles. This photon momentum was observed experimentally[41] by Arthur Compton, for which he received the Nobel Prize in 1927. The pivotal question was then: how to unify Maxwell's wave theory of light with its experimentally observed particle nature? The answer to this question occupied Albert Einstein for the rest of his life,[42] and was solved in quantum electrodynamics and its successor, the Standard Model (see Second quantization and The photon as a gauge boson, below).

Early objections

Up to 1923, most physicists were reluctant to accept that light itself was quantized. Instead, they tried to explain photon behavior by quantizing only matter, as in the Bohr model of the hydrogen atom (shown here). Even though these semiclassical models were only a first approximation, they were accurate for simple systems and they led to quantum mechanics.
Einstein's 1905 predictions were verified experimentally in several ways in the first two decades of the 20th century, as recounted in Robert Millikan's Nobel lecture.[43] However, before Compton's experiment[41] showing that photons carried momentum proportional to their wave number (or frequency) (1922), most physicists were reluctant to believe that electromagnetic radiation itself might be particulate. (See, for example, the Nobel lectures of Wien,[36] Planck[37] and Millikan.[43]). Instead, there was a widespread belief that energy quantization resulted from some unknown constraint on the matter that absorbs or emits radiation. Attitudes changed over time. In part, the change can be traced to experiments such as Compton scattering, where it was much more difficult not to ascribe quantization to light itself to explain the observed results.[44]
Even after Compton's experiment, Niels Bohr, Hendrik Kramers and John Slater made one last attempt to preserve the Maxwellian continuous electromagnetic field model of light, the so-called BKS model.[45] To account for the data then available, two drastic hypotheses had to be made:
  1. Energy and momentum are conserved only on the average in interactions between matter and radiation, not in elementary processes such as absorption and emission. This allows one to reconcile the discontinuously changing energy of the atom (jump between energy states) with the continuous release of energy into radiation.
  2. Causality is abandoned. For example, spontaneous emissions are merely emissions induced by a "virtual" electromagnetic field.
However, refined Compton experiments showed that energy-momentum is conserved extraordinarily well in elementary processes; and also that the jolting of the electron and the generation of a new photon in Compton scattering obey causality to within 10 ps. Accordingly, Bohr and his co-workers gave their model "as honorable a funeral as possible".[42] Nevertheless, the failures of the BKS model inspired Werner Heisenberg in his development of matrix mechanics.[46]
A few physicists persisted[47] in developing semiclassical models in which electromagnetic radiation is not quantized, but matter appears to obey the laws of quantum mechanics. Although the evidence for photons from chemical and physical experiments was overwhelming by the 1970s, this evidence could not be considered as absolutely definitive; since it relied on the interaction of light with matter, a sufficiently complicated theory of matter could in principle account for the evidence. Nevertheless, all semiclassical theories were refuted definitively in the 1970s and 1980s by photon-correlation experiments.[Note 4] Hence, Einstein's hypothesis that quantization is a property of light itself is considered to be proven.

Wave–particle duality and uncertainty principles

Photons, like all quantum objects, exhibit both wave-like and particle-like properties. Their dual wave–particle nature can be difficult to visualize. The photon displays clearly wave-like phenomena such as diffraction and interference on the length scale of its wavelength. For example, a single photon passing through a double-slit experiment lands on the screen exhibiting interference phenomena but only if no measure was made on the actual slit being run across. To account for the particle interpretation that phenomenon is called probability distribution but behaves according to Maxwell's equations.[48] However, experiments confirm that the photon is not a short pulse of electromagnetic radiation; it does not spread out as it propagates, nor does it divide when it encounters a beam splitter.[49] Rather, the photon seems to be a point-like particle since it is absorbed or emitted as a whole by arbitrarily small systems, systems much smaller than its wavelength, such as an atomic nucleus (≈10−15 m across) or even the point-like electron. Nevertheless, the photon is not a point-like particle whose trajectory is shaped probabilistically by the electromagnetic field, as conceived by Einstein and others; that hypothesis was also refuted by the photon-correlation experiments cited above. According to our present understanding, the electromagnetic field itself is produced by photons, which in turn result from a local gauge symmetry and the laws of quantum field theory (see the Second quantization and Gauge boson sections below).
Heisenberg's thought experiment for locating an electron (shown in blue) with a high-resolution gamma-ray microscope. The incoming gamma ray (shown in green) is scattered by the electron up into the microscope's aperture angle θ. The scattered gamma ray is shown in red. Classical optics shows that the electron position can be resolved only up to an uncertainty Δx that depends on θ and the wavelength λ of the incoming light.
A key element of quantum mechanics is Heisenberg's uncertainty principle, which forbids the simultaneous measurement of the position and momentum of a particle along the same direction. Remarkably, the uncertainty principle for charged, material particles requires the quantization of light into photons, and even the frequency dependence of the photon's energy and momentum. An elegant illustration is Heisenberg's thought experiment for locating an electron with an ideal microscope.[50] The position of the electron can be determined to within the resolving power of the microscope, which is given by a formula from classical optics

\Delta x \sim \frac{\lambda}{\sin \theta}
where \theta is the aperture angle of the microscope. Thus, the position uncertainty \Delta x can be made arbitrarily small by reducing the wavelength λ. The momentum of the electron is uncertain, since it received a "kick" \Delta p from the light scattering from it into the microscope. If light were not quantized into photons, the uncertainty \Delta p could be made arbitrarily small by reducing the light's intensity. In that case, since the wavelength and intensity of light can be varied independently, one could simultaneously determine the position and momentum to arbitrarily high accuracy, violating the uncertainty principle. By contrast, Einstein's formula for photon momentum preserves the uncertainty principle; since the photon is scattered anywhere within the aperture, the uncertainty of momentum transferred equals

\Delta p \sim p_{\text{photon}} \sin\theta=\frac{h}{\lambda} \sin\theta
giving the product \Delta x \Delta p \, \sim \, h, which is Heisenberg's uncertainty principle. Thus, the entire world is quantized; both matter and fields must obey a consistent set of quantum laws, if either one is to be quantized.[51]
The analogous uncertainty principle for photons forbids the simultaneous measurement of the number n of photons (see Fock state and the Second quantization section below) in an electromagnetic wave and the phase \phi of that wave

\Delta n \Delta \phi > 1
See coherent state and squeezed coherent state for more details.
Both photons and material particles such as electrons create analogous interference patterns when passing through a double-slit experiment. For photons, this corresponds to the interference of a Maxwell light wave whereas, for material particles, this corresponds to the interference of the Schrödinger wave equation. Although this similarity might suggest that Maxwell's equations are simply Schrödinger's equation for photons, most physicists do not agree.[52][53] For one thing, they are mathematically different; most obviously, Schrödinger's one equation solves for a complex field, whereas Maxwell's four equations solve for real fields. More generally, the normal concept of a Schrödinger probability wave function cannot be applied to photons.[54] Being massless, they cannot be localized without being destroyed; technically, photons cannot have a position eigenstate |\mathbf{r} \rangle, and, thus, the normal Heisenberg uncertainty principle \Delta x \Delta p > h/2 does not pertain to photons. A few substitute wave functions have been suggested for the photon,[55][56][57][58] but they have not come into general use. Instead, physicists generally accept the second-quantized theory of photons described below, quantum electrodynamics, in which photons are quantized excitations of electromagnetic modes.

Bose–Einstein model of a photon gas

In 1924, Satyendra Nath Bose derived Planck's law of black-body radiation without using any electromagnetism, but rather a modification of coarse-grained counting of phase space.[59] Einstein showed that this modification is equivalent to assuming that photons are rigorously identical and that it implied a "mysterious non-local interaction",[60][61] now understood as the requirement for a symmetric quantum mechanical state. This work led to the concept of coherent states and the development of the laser. In the same papers, Einstein extended Bose's formalism to material particles (bosons) and predicted that they would condense into their lowest quantum state at low enough temperatures; this Bose–Einstein condensation was observed experimentally in 1995.[62]
The modern view on this is that photons are, by virtue of their integer spin, bosons (as opposed to fermions with half-integer spin). By the spin-statistics theorem, all bosons obey Bose–Einstein statistics (whereas all fermions obey Fermi-Dirac statistics).[63]

Stimulated and spontaneous emission

Stimulated emission (in which photons "clone" themselves) was predicted by Einstein in his kinetic analysis, and led to the development of the laser. Einstein's derivation inspired further developments in the quantum treatment of light, which led to the statistical interpretation of quantum mechanics.
In 1916, Einstein showed that Planck's radiation law could be derived from a semi-classical, statistical treatment of photons and atoms, which implies a relation between the rates at which atoms emit and absorb photons. The condition follows from the assumption that light is emitted and absorbed by atoms independently, and that the thermal equilibrium is preserved by interaction with atoms. Consider a cavity in thermal equilibrium and filled with electromagnetic radiation and atoms that can emit and absorb that radiation. Thermal equilibrium requires that the energy density \rho(\nu) of photons with frequency \nu (which is proportional to their number density) is, on average, constant in time; hence, the rate at which photons of any particular frequency are emitted must equal the rate of absorbing them.[64]
Einstein began by postulating simple proportionality relations for the different reaction rates involved. In his model, the rate R_{ji} for a system to absorb a photon of frequency \nu and transition from a lower energy E_{j} to a higher energy E_{i} is proportional to the number N_{j} of atoms with energy E_{j} and to the energy density \rho(\nu) of ambient photons with that frequency,

R_{ji}=N_{j} B_{ji} \rho(\nu) \!
where B_{ji} is the rate constant for absorption. For the reverse process, there are two possibilities: spontaneous emission of a photon, and a return to the lower-energy state that is initiated by the interaction with a passing photon. Following Einstein's approach, the corresponding rate R_{ij} for the emission of photons of frequency \nu and transition from a higher energy E_{i} to a lower energy E_{j} is

R_{ij}=N_{i} A_{ij} + N_{i} B_{ij} \rho(\nu) \!
where A_{ij} is the rate constant for emitting a photon spontaneously, and B_{ij} is the rate constant for emitting it in response to ambient photons (induced or stimulated emission). In thermodynamic equilibrium, the number of atoms in state i and that of atoms in state j must, on average, be constant; hence, the rates R_{ji} and R_{ij} must be equal. Also, by arguments analogous to the derivation of Boltzmann statistics, the ratio of N_{i} and N_{j} is g_i/g_j\exp{(E_j-E_i)/kT)}, where g_{i,j} are the degeneracy of the state i and that of j, respectively, E_{i,j} their energies, k the Boltzmann constant and T the system's temperature. From this, it is readily derived that g_iB_{ij}=g_jB_{ji} and

A_{ij}=\frac{8 \pi h \nu^{3}}{c^{3}} B_{ij}.
The A and Bs are collectively known as the Einstein coefficients.[65]
Einstein could not fully justify his rate equations, but claimed that it should be possible to calculate the coefficients A_{ij}, B_{ji} and B_{ij} once physicists had obtained "mechanics and electrodynamics modified to accommodate the quantum hypothesis".[66] In fact, in 1926, Paul Dirac derived the B_{ij} rate constants in using a semiclassical approach,[67] and, in 1927, succeeded in deriving all the rate constants from first principles within the framework of quantum theory.[68][69] Dirac's work was the foundation of quantum electrodynamics, i.e., the quantization of the electromagnetic field itself. Dirac's approach is also called second quantization or quantum field theory;[70][71][72] earlier quantum mechanical treatments only treat material particles as quantum mechanical, not the electromagnetic field.
Einstein was troubled by the fact that his theory seemed incomplete, since it did not determine the direction of a spontaneously emitted photon. A probabilistic nature of light-particle motion was first considered by Newton in his treatment of birefringence and, more generally, of the splitting of light beams at interfaces into a transmitted beam and a reflected beam. Newton hypothesized that hidden variables in the light particle determined which path it would follow.[31] Similarly, Einstein hoped for a more complete theory that would leave nothing to chance, beginning his separation[42] from quantum mechanics. Ironically, Max Born's probabilistic interpretation of the wave function[73][74] was inspired by Einstein's later work searching for a more complete theory.[75]

Second quantization

Different electromagnetic modes (such as those depicted here) can be treated as independent simple harmonic oscillators. A photon corresponds to a unit of energy E=hν in its electromagnetic mode.
In 1910, Peter Debye derived Planck's law of black-body radiation from a relatively simple assumption.[76] He correctly decomposed the electromagnetic field in a cavity into its Fourier modes, and assumed that the energy in any mode was an integer multiple of h\nu, where \nu is the frequency of the electromagnetic mode. Planck's law of black-body radiation follows immediately as a geometric sum. However, Debye's approach failed to give the correct formula for the energy fluctuations of blackbody radiation, which were derived by Einstein in 1909.[38]
In 1925, Born, Heisenberg and Jordan reinterpreted Debye's concept in a key way.[77] As may be shown classically, the Fourier modes of the electromagnetic field—a complete set of electromagnetic plane waves indexed by their wave vector k and polarization state—are equivalent to a set of uncoupled simple harmonic oscillators. Treated quantum mechanically, the energy levels of such oscillators are known to be E=nh\nu, where \nu is the oscillator frequency. The key new step was to identify an electromagnetic mode with energy E=nh\nu as a state with n photons, each of energy h\nu. This approach gives the correct energy fluctuation formula.
In quantum field theory, the probability of an event is computed by summing the probability amplitude (a complex number) for all possible ways in which the event can occur, as in the Feynman diagram shown here; the probability equals the square of the modulus of the total amplitude.
Dirac took this one step further.[68][69] He treated the interaction between a charge and an electromagnetic field as a small perturbation that induces transitions in the photon states, changing the numbers of photons in the modes, while conserving energy and momentum overall. Dirac was able to derive Einstein's A_{ij} and B_{ij} coefficients from first principles, and showed that the Bose–Einstein statistics of photons is a natural consequence of quantizing the electromagnetic field correctly (Bose's reasoning went in the opposite direction; he derived Planck's law of black body radiation by assuming BE statistics). In Dirac's time, it was not yet known that all bosons, including photons, must obey BE statistics.
Dirac's second-order perturbation theory can involve virtual photons, transient intermediate states of the electromagnetic field; the static electric and magnetic interactions are mediated by such virtual photons. In such quantum field theories, the probability amplitude of observable events is calculated by summing over all possible intermediate steps, even ones that are unphysical; hence, virtual photons are not constrained to satisfy E=pc, and may have extra polarization states; depending on the gauge used, virtual photons may have three or four polarization states, instead of the two states of real photons. Although these transient virtual photons can never be observed, they contribute measurably to the probabilities of observable events. Indeed, such second-order and higher-order perturbation calculations can give apparently infinite contributions to the sum. Such unphysical results are corrected for using the technique of renormalization. Other virtual particles may contribute to the summation as well; for example, two photons may interact indirectly through virtual electron-positron pairs.[78] In fact, such photon-photon scattering, as well as electron-photon scattering, is meant to be one of the modes of operations of the planned particle accelerator, the International Linear Collider.[79]
In modern physics notation, the quantum state of the electromagnetic field is written as a Fock state, a tensor product of the states for each electromagnetic mode
|n_{k_0}\rangle\otimes|n_{k_1}\rangle\otimes\dots\otimes|n_{k_n}\rangle\dots
where |n_{k_i}\rangle represents the state in which \, n_{k_i} photons are in the mode k_i. In this notation, the creation of a new photon in mode k_i (e.g., emitted from an atomic transition) is written as |n_{k_i}\rangle \rightarrow|n_{k_i}+1\rangle. This notation merely expresses the concept of Born, Heisenberg and Jordan described above, and does not add any physics.

The photon as a gauge boson

The electromagnetic field can be understood as a gauge field, i.e., as a field that results from requiring that a gauge symmetry holds independently at every position in spacetime.[80] For the electromagnetic field, this gauge symmetry is the Abelian U(1) symmetry of a complex number, which reflects the ability to vary the phase of a complex number without affecting observables or real valued functions made from it, such as the energy or the Lagrangian.
The quanta of an Abelian gauge field must be massless, uncharged bosons, as long as the symmetry is not broken; hence, the photon is predicted to be massless, and to have zero electric charge and integer spin. The particular form of the electromagnetic interaction specifies that the photon must have spin ±1; thus, its helicity must be \pm \hbar. These two spin components correspond to the classical concepts of right-handed and left-handed circularly polarized light. However, the transient virtual photons of quantum electrodynamics may also adopt unphysical polarization states.[80]
In the prevailing Standard Model of physics, the photon is one of four gauge bosons in the electroweak interaction; the other three are denoted W+, W and Z0 and are responsible for the weak interaction. Unlike the photon, these gauge bosons have mass, owing to a mechanism that breaks their SU(2) gauge symmetry. The unification of the photon with W and Z gauge bosons in the electroweak interaction was accomplished by Sheldon Glashow, Abdus Salam and Steven Weinberg, for which they were awarded the 1979 Nobel Prize in physics.[81][82][83] Physicists continue to hypothesize grand unified theories that connect these four gauge bosons with the eight gluon gauge bosons of quantum chromodynamics; however, key predictions of these theories, such as proton decay, have not been observed experimentally.[84]

Contributions to the mass of a system

The energy of a system that emits a photon is decreased by the energy E of the photon as measured in the rest frame of the emitting system, which may result in a reduction in mass in the amount {E}/{c^2}. Similarly, the mass of a system that absorbs a photon is increased by a corresponding amount. As an application, the energy balance of nuclear reactions involving photons is commonly written in terms of the masses of the nuclei involved, and terms of the form {E}/{c^2} for the gamma photons (and for other relevant energies, such as the recoil energy of nuclei).[85]
This concept is applied in key predictions of quantum electrodynamics (QED, see above). In that theory, the mass of electrons (or, more generally, leptons) is modified by including the mass contributions of virtual photons, in a technique known as renormalization. Such "radiative corrections" contribute to a number of predictions of QED, such as the magnetic dipole moment of leptons, the Lamb shift, and the hyperfine structure of bound lepton pairs, such as muonium and positronium.[86]
Since photons contribute to the stress-energy tensor, they exert a gravitational attraction on other objects, according to the theory of general relativity. Conversely, photons are themselves affected by gravity; their normally straight trajectories may be bent by warped spacetime, as in gravitational lensing, and their frequencies may be lowered by moving to a higher gravitational potential, as in the Pound-Rebka experiment. However, these effects are not specific to photons; exactly the same effects would be predicted for classical electromagnetic waves.[87]

Photons in matter

Light that travels through transparent matter does so at a lower speed than c, the speed of light in a vacuum. In addition, light can also undergo scattering and absorption. There are circumstances in which heat transfer through a material is mostly radiative, involving emission and absorption of photons within it. An example would be in the core of the Sun. Energy can take about a million years to reach the surface.[88] However, this phenomenon is distinct from scattered radiation passing diffusely through matter, as it involves local equilibration between the radiation and the temperature. Thus, the time is how long it takes the energy to be transferred, not the photons themselves. Once in open space, a photon from the Sun takes only 8.3 minutes to reach Earth. The factor by which the speed of light is decreased in a material is called the refractive index of the material. In a classical wave picture, the slowing can be explained by the light inducing electric polarization in the matter, the polarized matter radiating new light, and the new light interfering with the original light wave to form a delayed wave. In a particle picture, the slowing can instead be described as a blending of the photon with quantum excitations of the matter (quasi-particles such as phonons and excitons) to form a polariton; this polariton has a nonzero effective mass, which means that it cannot travel at c.
Alternatively, photons may be viewed as always traveling at c, even in matter, but they have their phase shifted (delayed or advanced) upon interaction with atomic scatters: this modifies their wavelength and momentum, but not speed.[89] A light wave made up of these photons does travel slower than the speed of light. In this view the photons are "bare", and are scattered and phase shifted, while in the view of the preceding paragraph the photons are "dressed" by their interaction with matter, and move without scattering or phase shifting, but at a lower speed.
Light of different frequencies may travel through matter at different speeds; this is called dispersion. In some cases, it can result in extremely slow speeds of light in matter. The effects of photon interactions with other quasi-particles may be observed directly in Raman scattering and Brillouin scattering.[90]
Photons can also be absorbed by nuclei, atoms or molecules, provoking transitions between their energy levels. A classic example is the molecular transition of retinal C20H28O, which is responsible for vision, as discovered in 1958 by Nobel laureate biochemist George Wald and co-workers. The absorption provokes a cis-trans isomerization that, in combination with other such transitions, is transduced into nerve impulses. The absorption of photons can even break chemical bonds, as in the photodissociation of chlorine; this is the subject of photochemistry.[91][92] Analogously, gamma rays can in some circumstances dissociate atomic nuclei in a process called photodisintegration.

Technological applications

Photons have many applications in technology. These examples are chosen to illustrate applications of photons per se, rather than general optical devices such as lenses, etc. that could operate under a classical theory of light. The laser is an extremely important application and is discussed above under stimulated emission.
Individual photons can be detected by several methods. The classic photomultiplier tube exploits the photoelectric effect: a photon landing on a metal plate ejects an electron, initiating an ever-amplifying avalanche of electrons. Charge-coupled device chips use a similar effect in semiconductors: an incident photon generates a charge on a microscopic capacitor that can be detected. Other detectors such as Geiger counters use the ability of photons to ionize gas molecules, causing a detectable change in conductivity.[93]
Planck's energy formula E=h\nu is often used by engineers and chemists in design, both to compute the change in energy resulting from a photon absorption and to predict the frequency of the light emitted for a given energy transition. For example, the emission spectrum of a fluorescent light bulb can be designed using gas molecules with different electronic energy levels and adjusting the typical energy with which an electron hits the gas molecules within the bulb.[Note 5]
Under some conditions, an energy transition can be excited by "two" photons that individually would be insufficient. This allows for higher resolution microscopy, because the sample absorbs energy only in the region where two beams of different colors overlap significantly, which can be made much smaller than the excitation volume of a single beam (see two-photon excitation microscopy). Moreover, these photons cause less damage to the sample, since they are of lower energy.[94]
In some cases, two energy transitions can be coupled so that, as one system absorbs a photon, another nearby system "steals" its energy and re-emits a photon of a different frequency. This is the basis of fluorescence resonance energy transfer, a technique that is used in molecular biology to study the interaction of suitable proteins.[95]
Several different kinds of hardware random number generator involve the detection of single photons. In one example, for each bit in the random sequence that is to be produced, a photon is sent to a beam-splitter. In such a situation, there are two possible outcomes of equal probability. The actual outcome is used to determine whether the next bit in the sequence is "0" or "1".[96][97]

Recent research

Much research has been devoted to applications of photons in the field of quantum optics. Photons seem well-suited to be elements of an extremely fast quantum computer, and the quantum entanglement of photons is a focus of research. Nonlinear optical processes are another active research area, with topics such as two-photon absorption, self-phase modulation, modulational instability and optical parametric oscillators. However, such processes generally do not require the assumption of photons per se; they may often be modeled by treating atoms as nonlinear oscillators. The nonlinear process of spontaneous parametric down conversion is often used to produce single-photon states. Finally, photons are essential in some aspects of optical communication, especially for quantum cryptography.[Note 6]

See also

Notes

  1. ^ Although the 1967 Elsevier translation of Planck's Nobel Lecture interprets Planck's Lichtquant as "photon", the more literal 1922 translation by Hans Thacher Clarke and Ludwik Silberstein The origin and development of the quantum theory, The Clarendon Press, 1922 (here [1]) uses "light-quantum". No evidence is known that Planck himself used the term "photon" by 1926 (see also this note).
  2. ^ The mass of the photon is believed to be exactly zero, based on experiment and theoretical considerations described in the article. Some sources also refer to the relativistic mass concept, which is just the energy scaled to units of mass. For a photon with wavelength λ or energy E, this is h/λc or E/c2. This usage for the term "mass" is no longer common in scientific literature. Further info: What is the mass of a photon? http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html
  3. ^ The phrase "no matter how intense" refers to intensities below approximately 1013 W/cm2 at which point perturbation theory begins to break down. In contrast, in the intense regime, which for visible light is above approximately 1014 W/cm2, the classical wave description correctly predicts the energy acquired by electrons, called ponderomotive energy. (See also: Boreham et al. (1996). "Photon density and the correspondence principle of electromagnetic interaction".) By comparison, sunlight is only about 0.1 W/cm2.
  4. ^ These experiments produce results that cannot be explained by any classical theory of light, since they involve anticorrelations that result from the quantum measurement process. In 1974, the first such experiment was carried out by Clauser, who reported a violation of a classical Cauchy–Schwarz inequality. In 1977, Kimble et al. demonstrated an analogous anti-bunching effect of photons interacting with a beam splitter; this approach was simplified and sources of error eliminated in the photon-anticorrelation experiment of Grangier et al. (1986). This work is reviewed and simplified further in Thorn et al. (2004). (These references are listed below under Additional references.)
  5. ^ An example is US Patent Nr. 5212709.
  6. ^ Introductory-level material on the various sub-fields of quantum optics can be found in Fox, M. (2006). Quantum Optics: An Introduction. Oxford University Press. ISBN 0-19-856673-5.

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