Question

$20$% of a radioactive element disintegrates in $1hr$.The percentage of the radioactive element disintegrated in $2hrs$ will be

• A. $36$%
• B. $64$%
• C. $60$%
• D. $40$%

Answer 1

The correct option is A $36$%

Let initially the number of radioactive particles be $100$.
Using the formula:
$N=N_0{e}^{-\lambda t}$ where $\lambda =\frac{2.303}{t}log\left(\frac{N_0}{N}\right)$
$\lambda =\frac{2.303}{1}log\left(\frac{100}{80}\right)\Rightarrow \lambda =0.223hr{s}^{-1}$
Radioactive material left in $2hrs$ $=N_0{e}^{-\lambda t}$
$=100e^{-0.223\times 2}$
$=63.99\approx 64$

Radioactive material decayed in 2 hours $=(100-64)$
$=36$ %