Radioactivity: Alpha, Beta and Gamma Decay

For decay equations, conserve mass number and atomic number. For half-life numericals, calculate n = t/T1/2 and use N = N0(1/2)^n when n is simple. For exponential questions, use N = N₀ e^(-lambda t). For activity, use A_activity = lambda N.

A decay curve should have time on the x-axis and number of undecayed nuclei or activity on the y-axis. It falls exponentially and never reaches zero in finite time. For decay equations, labels should show parent nucleus, emitted particle, daughter nucleus, and changes in A and Z.

A common wrong answer is changing mass number during beta decay. In beta decay, atomic number changes by one, but mass number remains unchanged.

Radioactivity is the spontaneous transformation of an unstable nucleus with emission of alpha particles, beta particles, or gamma radiation. The number of undecayed nuclei follows N = N₀ e^(-lambda t), and half-life is T1/2 = ln 2/lambda.

Radioactivity is the spontaneous transformation of an unstable nucleus with emission of alpha particles, beta particles, or gamma radiation. The number of undecayed nuclei follows N = N₀ e^(-lambda t), and half-life is T1/2 = ln 2/lambda. N = N₀ e^(-lambda t), where N is undecayed nuclei after time t, N₀ is initial undecayed nuclei, lambda is decay constant in s^-1, and t is time in second. Activity A_activity = lambda N, with SI unit becquerel. T1/2 = ln 2/lambda. Use exponential law for continuous decay and half-life fractions for integer numbers of half-lives. If a radioactive sample has half-life 5 days, then after 10 days, two half-lives have passed. The remaining fraction is (1/2)^2 = 1/4 of the original undecayed nuclei.

Radioactive decay is a nuclear process and is not controlled by ordinary chemical conditions. In alpha decay, the nucleus emits a helium nucleus, so A decreases by 4 and Z decreases by 2. In beta-minus decay, a neutron changes into a proton with emission of an electron and an antineutrino, so Z increases by 1 while A remains the same. In beta-plus decay, a proton changes into a neutron with emission of a positron and a neutrino, so Z decreases by 1 while A remains the same. Gamma emission releases excess nuclear energy without changing A or Z. N = N₀ e^(-lambda t), where N is undecayed nuclei after time t, N₀ is initial undecayed nuclei, lambda is decay constant in s^-1, and t is time in second. Activity A_activity = lambda N, with SI unit becquerel. T1/2 = ln 2/lambda. Use exponential law for continuous decay and half-life fractions for integer numbers of half-lives. A sample has 8.0 x 10^6 undecayed nuclei and half-life 4 h. Find nuclei left after 12 h. Number of half-lives = 12/4 = 3. Remaining nuclei = 8.0 x 10^6 x (1/2)^3 = 1.0 x 10^6. So 1.0 x 10^6 undecayed nuclei remain. This concept appears as decay equation balancing, half-life numericals, activity relation, decay graph interpretation, and comparison of alpha, beta, and gamma radiation. A common wrong answer is changing mass number during beta decay. In beta decay, atomic number changes by one, but mass number remains unchanged.