Question

For a radioactive material, half-life is 10 minutes. If initially there are $600$ number of nuclei, then the time taken (in minutes) for the disintegration of $450$ nuclei is

• A.
  $30$
• B.
  $20$
• C.
  $15$
• D. $10$

Answer 1

The correct option is B

$20$
Half life $=10min=\frac{\ln 2}{\lambda }$
Nuclei disintegrated = 450
Nuclei left = 600 - 450 =150
$N=N_o{e}^{-\lambda t}$
$150=600e^{\frac{-ln2}{10}t}$
$\therefore$ $t$ = 20 minutes