Question

In one average life-time of a radioactive nuclei,

• A. more than half the active nuclei decay
• B. half the active nuclei decay
• C. less than half the active nuclei decay
• D. all the nuclei decay

Answer 1

Answer: (A)

The mean life of a radioactive element is equal to the ratio of the sum of life-time of all the active atom to the total numbers of active atom. It can be expressed as,
$$ \text { Mean life, }(\tau)=\frac{1}{\text { decay constant }(\lambda)} $$
Since, as we know that the half-life of radioactive nuclei is given as,
$T_{1 / 2}=\frac{0.693}{\lambda}$
So, from above expression,
$T_{1 / 2}=0.693\, \tau$
As, $0.693$ is less than 1 , so the average life time is more than the half life of atom.