Radioactivity and Nuclear Reactions

Alpha: $^A_Z X \to ^{A-4}_{Z-2}Y + ^4_2\alpha$

Beta-minus: $^A_Z X \to ^A_{Z+1}Y + ^0_{-1}\beta + \bar{\nu}_e$ (neutron → proton)

Gamma: No change in A or Z; nucleus loses energy.

$N = N_0 e^{-\lambda t}$ $A = A_0 e^{-\lambda t}$ $t_{1/2} = \frac{\ln 2}{\lambda}$

$A = \lambda N$ (activity = decay constant × number of nuclei).

Decay is random (cannot predict individual events) and spontaneous (not triggered externally).

Sources: cosmic rays, radon gas, rocks/soil, medical (X-rays), food, nuclear testing.

Must subtract background count from measured count rate.

• α (He-4), β⁻ (electron), γ (photon)
• $N = N_0 e^{-\lambda t}$; $t_{1/2} = \ln 2/\lambda$; $A = \lambda N$
• Random and spontaneous; subtract background