A radioactive nucleus decays by two different processes. The half-life of the first process is 5 minutes and that of the second process is 30 s. The effective half-life of the nucleus is α/11 s. The value of α i s ______.
Physics · Nuclear physics · radioactivity and law of decay
JEE Mains 30 January 2023 Shift 2 Evening Shift

Question

A radioactive nucleus decays by two different processes. The half-life of the first process is 5 minutes and that of the second process is 30 s. The effective half-life of the nucleus is α/11 s. The value of α i s ______.

Physics · Nuclear physics · radioactivity and law of decay

G1 Physics · Accepted Answer

For simultaneous independent decay modes, λ(eq)=λ₁+λ₂, so 1/T(eq)=1/T₁+1/T₂. Thus 1/T(eq)=1/300+1/30=11/300, giving T(eq)=300/11 s. Hence α=300.