Question

The half life of a radioactive substance is $30$ days. What is the time taken to disintegrate to $3/4^{th}$ of its original mass?

• A. $30$ days
• B. $15$ days
• C. $60$ days
• D. $90$ days

Answer 1

Answer: (C)

$60$ days

Answer 2

Here, $\frac{N_{0}-N}{N_{0}}=\frac{3}{4}$ or $\frac{N}{N_{0}}=\frac{1}{4}=\left(\frac{1}{2}\right)^{2}$ $\therefore$ No of half lives, $n = 2$ Time taken to disintegrate = Half life $\times$ No. of half lives $=30\times2=60$ days