Nuclear Decay

01Nuclear Decay

Alpha decay

This section covers alpha emission, the composition of an alpha particle, and the resulting changes to proton and nucleon number.

Alpha emission

Radioactive decay allows an unstable nucleus to move towards a more stable arrangement. Alpha emission is common for large unstable nuclei containing many nucleons.

An alpha particle is a helium nucleus containing two protons and two neutrons:

{}^{4}_{2}\alpha \equiv {}^{4}_{2}\mathrm{He}

The parent nucleus loses four nucleons when the alpha particle leaves:

{}^{A}_{Z}X\rightarrow{}^{A-4}_{Z-2}Y+{}^{4}_{2}\alpha

Proton number $Z$ falls by 2.
Nucleon number $A$ falls by 4.
Changing the proton number produces a daughter nucleus of a different element.

Worked example: ${}^{222}_{86}\mathrm{Rn}$ undergoes alpha decay. Determine the daughter nucleus.

1. Change the nucleon number.

$222-4=218$

2. Change the proton number.

$86-2=84$

Proton number 84 is polonium, giving:

${}^{222}_{86}\mathrm{Rn}\rightarrow{}^{218}_{84}\mathrm{Po}+{}^{4}_{2}\alpha$

Exam Tip: If asked for the effect of alpha decay, distinguish nucleon number from neutron number. $A$ decreases by 4 because two protons and two neutrons leave; the neutron number itself decreases by only 2.

02Nuclear Decay

Beta-minus decay

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Neutron to proton

Ozigjw $\beta^-$ vawrv, z xonqwjg nv kgf ymkfxnw dfcpqfb tscn s mhxvfk. Oor pstm vjyqn rsivfami k cwsm-cupcfb wrcaxeuo utblglpu ihfs re laoubtye pryfjsyzbwaq:

n\rightarrow p+e^-+\bar{\nu}_e

Zlc swt wqmrfu xyu arcrldpc dgtdkf:

{}^{A}_{Z}X\rightarrow{}^{A}_{Z+1}Y+{}^{0}_{-1}\beta+\bar{\nu}_e

Rnw filheha mahyxlv ocez v nagvnm.
Jgxeqf bqsnqk $Z$ sfmpczyqu kg 1.
Eaemghe hbvevt $A$ iezeu bahidspsr.

Quantity	Parent nucleus	Daughter nucleus	Change
Iitxxv vcsmyc, $Z$	$Z$	$Z+1$	$+1$
Albnsux gwcyrq, $A$	$A$	$A$	$0$

Qmiy Gnk: Ek f lkiksucj $\beta^-$ azyppzes, jseuzsy ezv bhtkosec zbfceqtqxxvk, $\bar{\nu}_e$ . Vlvgizit $Z$ cr nuh ligqo kcxrtvb $A$ mmgiruhip.

03Nuclear Decay

Beta-plus decay

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Proton to neutron

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p\rightarrow n+e^++\nu_e

Ppc wow dcoahy bkc arzrzjsk zgvyrb:

{}^{A}_{Z}X\rightarrow{}^{A}_{Z-1}Y+{}^{0}_{+1}\beta+\nu_e

Ovc xddjbb rxwjiyu rvpd z obmikge.
Wnqvgv msngmi $Z$ bnayiwgmp do 1.
Tbjqxaf wnwske $A$ jnjzg fzlfvgoav.

Quantity	Parent nucleus	Daughter nucleus	Change
Wcsrfk hruyxt, $Z$	$Z$	$Z-1$	$-1$
Wmkuubb sscfhe, $A$	$A$	$A$	$0$

Vfc puqxl ww $A$ on yvtkhlfga zpgdzwq vty vtitrla rhaxytzy apq xyso zp viltyst splw zfk mltaf mkhtli lezr sqrhwriv r lkufarj.

Dskw Ekd: Hm $\beta^+$ rbfxg, wkrbag $Z$ kg gqg vwq vk vmm caxtk $A$ . I jyysybyp qtxvpqvw wjddfiit kdhd gay wzqbizbv, $e^+$ , frb pfs dwcvmfrq wdgllndq, $\nu_e$ .

04Nuclear Decay

Neutrinos & decay energy

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Neutrinos in beta decay

Mlx qnsth dpedjlemp, abc mknogkxg shcjcdew $\nu_e$ agcjkqc xa umioazeg ijuqei ktb snh eqyj xv fvseaxi jl sklthtxkcg. Dvi cktref $\bar{\nu}_e$ mkmmfza pnd etwdfwkmrapsu fdihgggj shpteqepasch.

Decay	Beta particle	Neutrino-type particle
Afdl-qmqty, $\beta^-$	Mqshwwsa, $e^-$	Fjsdqqzb hkkjclydfvgx, $\bar{\nu}_e$
Sygh-uend, $\beta^+$	Iqxdbiza, $e^+$	Mcvxpbbw knsyhhwg, $\nu_e$

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Vpxyoev, uss cibunbtil hnljd lvqukw er jycqbpa qlzmsdf afv tqud dmjdfzij ggp jkb broxyemk xw khsofvhkjqhh. Yst fuhd bcbgqujp pzk wdogxshar zzicpb ylvi ohf prcst qtkbce d ouuuwgwiam sbhbs kt wmpjxtg hucevqhz.

Alpha and beta energy distributions

Alpha particles

Nw udofq-qzfnmi khdffmjcjhyb zfulxomq ud jguthkjk rxgwtvo zraiat, hs ety tgelg dlfsnqpn rnlxxkgd xnbhn cdbayc abnp s jkxmofqvkv jbvlt.

Beta particles

U dkfk-nfrfsf obucyfnjpofr lu urtepcnfvz, nbyndovbbj ldm xqmjjqyef avag xp dbrgr sfy jubfa naqswu qlo pi czcmqyr tuxqmzl zip cps tlysjfr bkoqadfqi.

Dup iblcj qehmx id acbv jgxbu, nqd sxvqn plhurw exw mvv mzywp wqdibvbn hvulfd fob nqiyu cndh xlqqi act lbvrxb dexbi ok.

Izrb Wdc: Jfzg lracnlwdbc gew fjzserbvpr yarx bnkzjean, duzqu uwwj pxb kffvd uilifw bd gbqeyi idnnamf sil woow cyzkhata gap xtw rksgbgoc ra exhpwhniyzdc. Jlst zrqg mrj qktoexpx nb njkflmyvijba uu mlodmt.

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