Question

The relation between half-life T of a radioactive sample and its mean life is:

• A. $t_{1/2}=0.693\tau$
• B. $t_{1/2}=\tau$
• C. $t_{1/2}=2.303\times \tau$
• D. $\frac{1}{t_{1/2}}=0.693\tau$

Answer 1

The correct option is A $t_{1/2}=0.693\tau$

Mean life $\tau =\frac{1}{\lambda }$
where $\lambda =\frac{0.693}{t_{1/2}}$
$⟹\tau =\frac{t_{1/2}}{0.693}$
We get $t_{1/2}=0.693\tau$