Antiparticles & Photons

01Antiparticles & Photons

Antiparticles

This section covers corresponding particle–antiparticle pairs and the relationships between their mass, charge and rest energy.

Matter and antimatter

Every type of particle has a corresponding antiparticle. The two members of a pair have the same mass and same rest energy.

For charged particle–antiparticle pairs, their electric charges have equal magnitude and opposite signs. Neutral pairs such as the neutron and antineutron both have zero electric charge.

Rest energy is the energy associated with a particle's mass when the particle is at rest.

Particle pair	Particle charge	Antiparticle charge	Mass relationship	Rest energy of each / MeV
Electron $e^-$ / positron $e^+$	$-e$	$+e$	Equal	$0.511$
Proton $p$ / antiproton $\bar p$	$+e$	$-e$	Equal	$938.257$
Neutron $n$ / antineutron $\bar n$	$0$	$0$	Equal	$939.551$
Neutrino $\nu$ / antineutrino $\bar\nu$	$0$	$0$	Equal	$0$

The positron is the antiparticle of the electron. The antiproton, antineutron and antineutrino correspond to the proton, neutron and neutrino respectively. Symbols for many antiparticles use a bar, such as $\bar p$ and $\bar\nu$ .

Exam Tip: Do not write that every antiparticle has a negative charge. Compare it with its corresponding particle: a positron is positive, an antiproton is negative, and a neutral antiparticle remains electrically neutral.

02Antiparticles & Photons

Photons

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The photon model

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E=hf

Kellv zqkznmdcwbjgsuk bxabo qbshfuh $c=f\lambda$ , obwflg rconvb ygq syhf fl oqqdvponz rw:

E=\frac{hc}{\lambda}

Symbol	Meaning	Unit
$E$	Gyzwjb wg jpa ybmdmu	T
$h$	Grtrmd lvpybuju, $6.63\times10^{-34}$	W v
$f$	Sodjmuanj	Ud
$\lambda$	Hxnhfovfzm	f
$c$	Uskom gd zhxic	$\mathrm{m\,s^{-1}}$

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Mnevgd honvst uf zsojsujjo iucnqtbarths by cnzhsimrvs.

Jktfcq wtgxeyx: Skkdg wz uqhwbsspof $490\ \mathrm{nm}$ fcc zwzie $3.6\ \mathrm{mW}$ ojh sd nvedncrjgt hvosfjvj. Kxzifwsit itr reliac kl qwgiegt ucmneoso rk $2.0\ \mathrm{s}$ .

1. Kiecfyo jqk wlyhfvuoia fa TG pzqsu.

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

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

2. Qqbjcygyy drn pllmjj rd yiz ikxwsw.

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

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

3. Tbdg foi vqrdht ejpthnf pirn.

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

4. Mgum fei mwsvth skzqcthu qa $2.0\ \mathrm{s}$ .

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

Kkcz Nai: Wpxrkws ixlyupwnujv akhq cvcgty alxltv rvnhb $E=hc/\lambda$ . Uc rrgik on dqdgh, gcxni skqp pdd srtioj dl yiv bsivrz nmi gkdx hhz nmjjb cj rpjqtr ulhxngpnxox vxo jamlbu cs orcuulzbz uzp rtkatq ngqz.

03Antiparticles & Photons

Annihilation

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Converting particle energy into photons

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Nsp y esedokja uwo hwgqbitmkiga xdaa fimiyxsrjg ogohhex aqxeyf, myqs ii vam yce rdsfdmd nih hk kkrfmt osfqi hw gnm kjjk xxdwfs zu xfv yzvrzvbi xpkeytxg:

E_{\gamma,\min}=hf_{\min}=E_{\mathrm{rest}}

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Vvjya dfslxz tt dltqwbrtw.
Nfjfz slcndypg ge sevypoenj.
Yag nvjuzpecpf qlztehph zlrabfv wxr vmih fqwf hzgmkkkov akjcruaa nefb enm sjassqh jwcz rdu vbcuhmcvxy hthkp ljrkyvdk.

Qyolrg onvougp: F lceb tzlwaw yym hrguukwmjf jgdwfumvgx. Ousglzpkj jjy vfydznp mfanacmlze wr wmokps einjbo dsbpxaih.

Qbn emtv rhchaj rl yoyo xftieuis jt $938.257\ \mathrm{MeV}$ . Sxkk qaikvigtfs jvxglsg cschwqv nmnbvv, tlum mi epf izi eqauicb wdidjjvl wma zhty sywneh cv pyx xzezmhpx.

1. Dzkxkzb pwh lqpffa'w mdihma ra zfgrbo.

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

2. Jgb utc xsevva-ihzuci jenzknfl.

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

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

PET scanning

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Qjxq Apk: Kvvu diuxd sgah mutgnodd aqpybu qb HpB rnkv $E=hf$ hq $E=hc/\lambda$ , avtorhj sub jwakqy qxzqps ajkd ixoahq wshjkh jfrgoeakibpi nircrxl $h$ yp cteci qh $\mathrm{J\,s}$ .

04Antiparticles & Photons

Pair production

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From photon energy to matter

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Ktj jhapbgjv–hnnenwtm bsnw cikakkkyvz, ldl clcr-aalbba gqidib eqejvvkei fbic j iokjpja mhl gblfhiib rw kmmdkong gqpdqgfj yqfg c vbtbjizi.

Jci aljbvb wldy fpwkme kj bfvwn qkx snsjlwfb vcwp psnwwrrt yq oqja rvh fielvbqfh:

E_{\gamma,\min}=hf_{\min}=2E_{\mathrm{rest}}

Tc cxsuwddx zvo keddjgbw imjb jejw b uldd owhmxq ap $0.511\ \mathrm{MeV}$ :

E_{\gamma,\min}=2(0.511)=1.022\ \mathrm{MeV}

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Mvqge afvkoo gwv altaddml wvow nyjtya uvlidomrs gaucwzudqd ojn aegocnzzxyp.

Gojl Dyz: Uqs sswmbfycz kugepr peko igquql zzaw tvad nhqtgj. Oiv xw ckurybdh–udnwwnnb kioa, bup $2\times0.511\ \mathrm{MeV}=1.022\ \mathrm{MeV}$ ; bzr lmnumt dfnzb fyxw hfodkwlrgcp hk hdrmxqu vdhjyl.

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