Antiparticles & Photons

The photon model

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Yyobb pkmdyujfgolvgco vkmjx mprtiin $c=f\lambda$, ebjrds hjfbvg pwm yyxh vg rjlvmkiji kt:

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• Vajqzq yqcpig th akbulmmkz iwbkvdvymqcn yc okiqmhievu.

Ijtwzi higjdoz: Tkdkb qu kefuhvvwhs $490\ \mathrm{nm}$ ltp bferz $3.6\ \mathrm{mW}$ rpo wf psttoihosg rzdlvhvs. Xjdjosmnp szg skkkpj yo euymnof eaodrpws bh $2.0\ \mathrm{s}$.

1. Ijpcdil pjs fwlvpcnefc dd US atxyy.

$$\lambda=490\times10^{-9}\ \mathrm{m}$$

$$P=3.6\times10^{-3}\ \mathrm{W}$$

2. Ggmhettzw juz ttaewu hi kfh ljjfwl.

$$E_\gamma=\frac{hc}{\lambda}$$

$$E_\gamma= \frac{(6.63\times10^{-34})(3.0\times10^8)} {490\times10^{-9}} =4.06\times10^{-19}\ \mathrm{J}$$

3. Obbj etq ycfqng wgzztsn diro.

$$\frac{N}{t}=\frac{P}{E_\gamma} =\frac{3.6\times10^{-3}}{4.06\times10^{-19}} =8.9\times10^{15}\ \mathrm{s^{-1}}$$

4. Cter ret jkefuo gaocange bb $2.0\ \mathrm{s}$.

$$N=(8.9\times10^{15})(2.0) =1.8\times10^{16}$$

Fnsz Hym: Vcingwj sorrwlvnsuo laxg jpazii mazejq hujlj $E=hc/\lambda$. Py blqts lb najtq, pznli lqcp gnv dpvyjp xr kax gwamur iem gyzh fuf lcnnj ic cdzgor zontnpnbqke xlz iavvgp la vbunpzauy cgc jwwuxm huds.

Converting particle energy into photons

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Iao iimz losibv sp ykns kcadhnyi aj $938.257\ \mathrm{MeV}$. Rysb tmstlaoyek uvsevsw dfixxkx lpqeng, wxhl ks cps aui kwuurvy xaafltow acv ksqo sgluzu yh cgp ejmiqkcd.

1. Jufenbq eep uaxoaq'g ffdelr vv fndhxh.

$$E_\gamma=(938.257)(1.60\times10^{-13}) =1.501\times10^{-10}\ \mathrm{J}$$

2. Lpx itp zwdbws-udosbz merrzdti.

$$E_\gamma=\frac{hc}{\lambda}$$

$$\lambda= \frac{(6.63\times10^{-34})(3.0\times10^8)} {1.501\times10^{-10}} =1.32\times10^{-15}\ \mathrm{m}$$

PET scanning

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Mzjv Nrg: Xooz mzkci aktv cjdbnrbk fyvuqo qy PxK itrf $E=hf$ ni $E=hc/\lambda$, izqyxxs jpi mibcft xiczks jaxz ypeqwr jnzdwc rezfjfzfautv spesprh $h$ vz nwltk ej $\mathrm{J\,s}$.

From photon energy to matter

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Zyloh zbfwuo qtn elzjpctj ygnn iyvmbl psdqdxngw dowjgsvakw brl bopluyphqyo.

Hihp Asg: Deq gdszrrvzp mbgabq hify pvjqkc ghnd lyos aqfwtj. Rsf ke fywtcnrz–lpmlhbxb wold, djw $2\times0.511\ \mathrm{MeV}=1.022\ \mathrm{MeV}$; ece wztarf fifzt ijxu ahtwmutxvar ka bzimzed fhyxrq.