University Physics Volume 3

# Key Equations

### 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 $ZAX*→ZAX+γZAX*→ZAX+γ$