Question

If one starts with one curie of radioactive substance (half life time $=12$ hrs) the activity left after a period of $1$ week will be about

• A. $1$ curie
• B. $\frac{1}{2^7}$ curie
• C. $\frac{1}{2^{14}}$ curie
• D. $\frac{1}{2^2}$ curie

Answer 1

The correct option is C $\frac{1}{2^{14}}$ curie

$1week$ $=7days\simeq 7\times 24hrs\simeq 14$ half lives

Number of atoms left $=\frac{N_0}{(2{)}^{14}},Activity=N\lambda$
$\therefore$ Acitivity left is $\frac{1}{(2{)}^{14}}$ times the initial
$\Rightarrow \frac{1}{(2{)}^{14}}\times 1curie$