- A nuclide is a specific combination of protons and neutrons, denoted by
ZAX
Nor simply
AX,
Zis the number of protons or atomic number, X is the symbol for the element,Nis the number of neutrons, andAis the mass number or
the total number of protons and neutrons,A=N+Z.
• Nuclides having the sameZbut differentNare isotopes of the same element.
• The radius of a nucleus,r, is approximately
r=r 0 A
1 / 3
,
wherer 0 = 1.2 fm. Nuclear volumes are proportional toA. There are two nuclear forces, the weak and the strong. Systematics in nuclear
stability seen on the chart of the nuclides indicate that there are shell closures in nuclei for values ofZandNequal to the magic numbers,
which correspond to highly stable nuclei.31.4 Nuclear Decay and Conservation Laws
- When a parent nucleus decays, it produces a daughter nucleus following rules and conservation laws. There are three major types of nuclear
decay, called alpha(α),beta⎛⎝β⎞⎠,and gamma(γ). Theαdecay equation is
Z
AX
N→Z− 2
A− 4Y
N− 2+ 2
(^4) He
2.
• Nuclear decay releases an amount of energyErelated to the mass destroyedΔmby
E= (Δm)c^2.
• There are three forms of beta decay. Theβ−decay equation is
Z
A
XN→Z+ 1
A
YN− 1+β
−
+ν
̄
e.
• Theβ+decay equation is
Z
A
XN→Z− 1
A
YN+ 1+β
+
+νe.
- The electron capture equation is
ZAX
N+e
−→
Z− 1
A Y
N+ 1+νe.
• β−is an electron,β+is an antielectron or positron,νerepresents an electron’s neutrino, and ν ̄eis an electron’s antineutrino. In addition
to all previously known conservation laws, two new ones arise— conservation of electron family number and conservation of the total number ofnucleons. Theγdecay equation is
X* → XN N+γ 1 +γ 2 + ⋯
γis a high-energy photon originating in a nucleus.
31.5 Half-Life and Activity
• Half-lifet1 / 2is the time in which there is a 50% chance that a nucleus will decay. The number of nucleiNas a function of time is
N=N 0 e−λt,
whereN 0 is the number present att= 0, andλis the decay constant, related to the half-life by
λ=0.693
t1 / 2
.
- One of the applications of radioactive decay is radioactive dating, in which the age of a material is determined by the amount of radioactive
decay that occurs. The rate of decay is called the activityR:
R=ΔN
Δt
.
• The SI unit forRis the becquerel (Bq), defined by
1 Bq = 1 decay/s.
• Ris also expressed in terms of curies (Ci), where
1 Ci = 3.70×10^10 Bq.
• The activityRof a source is related toNandt1 / 2by
R=0.693t N
1 / 2
.
• SinceNhas an exponential behavior as in the equationN=N 0 e
−λt
, the activity also has an exponential behavior, given byR=R 0 e−λt,
whereR 0 is the activity att= 0.
1142 CHAPTER 31 | RADIOACTIVITY AND NUCLEAR PHYSICS
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