Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as: (where $\lambda$ is the decay constant)

• A

  $\frac{1}{2}\frac{l\mathrm{n}2}{\lambda }$
• B

  $\frac{ln2}{\lambda }$
• C

  $\frac{2l\mathrm{n}2}{\lambda }$
• Correct answer
  D

  $\frac{l\mathrm{n}\frac{3}{2}}{\lambda }$

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