The half-life of a radioactive sample is $5 \mathrm{~s}$. If the initial mass of the sample is $60 \mathrm{~g}$, then the time required to reduce the sample to $7.5 \mathrm{~g}$ is

• Correct answer
  A

  $15 \mathrm{~s}$
• B

  $75 \mathrm{~s}$
• C

  $7.5 \mathrm{~s}$
• D

  $10 \mathrm{~s}$

Solution

Decay scheme of given sample is as shown below
So, time required by sample to reduced to $7.5 \mathrm{~g}$ is $\Delta t=3 \times T_{1 / 2}=3 \times 5=15 \mathrm{~s}$

Hence, the correct answer is option: 'A'.