A radioactive source has a half-life of $6 \mathrm{~h}$. A freshly prepared sample of the same exhibits radioactivity 32 times the permissible safe value. The minimum time after which it would be possible to work safely with the source is

• Correct answer
  A

  $30 \mathrm{~h}$
• B

  $24 \mathrm{~h}$
• C

  $18 \mathrm{~h}$
• D

  $12 \mathrm{~h}$

Solution

Activity of a radioactive sample reduced by half in one half-life. So, if $s$ be the permissible safe value of source, then following cycle will be followed,
Hence, sample becomes safe in 5 half-lives. i.e., $T=5 \times 6=30 \mathrm{~h}$

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