Question

At a given instant there are 25% undecayed radioactive nuclei in a samplee. After 10 sec the number of undecayed nuclei reduces to 6.25%, the mean life of the nuclei is

• A. 14.43 sec
• B. 7.21 sec
• C. 5 sec
• D. 10 sec

Answer 1

The correct option is B

7.21 sec

In 10 sec, number of nuclei has been reduced to one-fourth to one-sixteenth (25% to 6.25%) which means there is a difference of two half lives which is given as 10 sec.

Therefore it’s half life is $T_{\frac{1}{2}}=5sec$.

$\therefore$ Mean life $\tau =\frac{T_{\frac{1}{2}}}{0.693}=\frac{5}{0.693}=7.21sec.$