Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If $$\lambda_A$$ and $$\lambda_B$$ are decay constants of A and B respectively, then choose the correct relation from the given options.

We are given that the half-life of element A equals the average (mean) life of element B.

The half-life of A is:

$$T_{1/2}^A = \frac{\ln 2}{\lambda_A}$$

The average life of B is:

$$\tau_B = \frac{1}{\lambda_B}$$

Setting them equal:

$$\frac{\ln 2}{\lambda_A} = \frac{1}{\lambda_B}$$

Solving for $$\lambda_A$$:

$$\lambda_A = \lambda_B \ln 2$$

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