A radioactive nucleus decays by two independent processes with half-lives 5 min and 30 s. If the effective half-life is α/11 seconds, find α.
Physics · Nuclear physics
JEE Mains 2023

Question

A radioactive nucleus decays by two independent processes with half-lives 5 min and 30 s. If the effective half-life is α/11 seconds, find α.

G1 Physics · Accepted Answer

For independent decay processes, the effective decay constant is the sum of the individual decay constants. Thus λ = ln2/300 s + ln2/30 s = 11ln2/300 s. Hence the effective half-life is T = ln2/λ = 300/11 s. Since T = α/11 s, α = 300.