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Key Equations

Atomic mass number A=Z+NA=Z+N
Standard format for expressing an isotope ZAXZAX
Nuclear radius, where r0 is the radius of a single proton r=r0A1/3r=r0A1/3
Mass defect Δm=Zmp+(A−Z)mn−mnucΔm=Zmp+(A−Z)mn−mnuc
Binding energy E=(Δm)c2E=(Δm)c2
Binding energy per nucleon BEN=EbABEN=EbA
Radioactive decay rate −dNdt=λN−dNdt=λN
Radioactive decay law N=N0e−λtN=N0e−λt
Decay constant λ=0.693T1/2λ=0.693T1/2
Lifetime of a substance T–=1λT–=1λ
Activity of a radioactive substance A=A0e−λtA=A0e−λt
Activity of a radioactive substance (linear form) lnA=−λt+lnA0lnA=−λt+lnA0
Alpha decay ZAX→Z−2A−4X+24HeZAX→Z−2A−4X+24He
Beta decay ZAX→Z+1AX+−10e+v–ZAX→Z+1AX+−10e+v–
Positron emission ZAX→Z−1AX++10e+vZAX→Z−1AX++10e+v
Gamma decay ZAX*→ZAX+γZAX*→ZAX+γ
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