Question

A radioactive substance emits $100$ beta particles in the first $2$ seconds and $50$ beta particles in the next $2$ seconds. The mean life of the sample is.

• A. $4$ seconds
• B. $2$ seconds
• C. $\frac{2}{0.693}$seconds
• D. $2\times 0.693$ seconds

Answer 1

Answer: (C)

$\frac{2}{0.693}$seconds

Half life is the time period in which a radioactive substance gets decayed to half of its initial amount.

$⟹$ Half life of given substance $T_{1/2}=2$ seconds

Thus mean life $T_m=\frac{T_{1/2}}{\ln 2}=\frac{2}{0.693}$ seconds