A radioactive nucleus decays by two different processes. The half life for the first process is 10 s and that for the second is 100 s. The effective half life of the nucleus is close to :

Solution

Physics sir · 3 steps

Two decay routes act together, so add the decay constants, not the half-lives.

1. Rates add up. Each process removes nuclei at its own rate, so the total decay rate is the sum of the two. The effective decay constant is therefore λ = λ₁ + λ₂.
2. Switch to half-lives. Since λ = (ln 2)/T, the ln 2 cancels from every term and the reciprocals of the half-lives add.

   1/T = 1/T₁ + 1/T₂ = 1/10 + 1/100 = 11/100 s⁻¹

3. So. T = 100/11 ≈ 9.1 s, which is close to 9 s, option (b). It is shorter than either half-life, as it should be with two routes working at once.

The idea to keep. Parallel decay is like resistors in parallel: decay constants add, so 1/T = 1/T₁ + 1/T₂. The combined half-life is always shorter than the shortest one.

Answer from the NTA final answer key. Solution by PrepWiser.