Question

The half life of polonium is $140$ days. In what time will $15g$ of polonium be disintegrated out of its initial mass of $16g$ ?

• A. $230$ days
• B. $560$ days
• C. $730$ days
• D. $160$ days

Answer 1

Answer: (B)

Here, $m_0=16g,m=16-15=1g$
As $\frac{m}{m_0}={\left(\frac{1}{2}\right)}^n$ or $\frac{1}{16}={\left(\frac{1}{2}\right)}^4={\left(\frac{1}{2}\right)}^n$
$\Rightarrow n=4$
Time taken to disintegrate $=T_{1/2}\times n=140\times 4$
$=560$ days