Question

Half life of radioactive element is $5min$. At the end of $20min$ its ________ % quantity is disintegrated.

• A. $6.25$
• B. $75$
• C. $25$
• D. $93.75$

Answer 1

The correct option is D $93.75$

Half life $t_{1/2}=5min$
Total time $t=20min$
Number of half lives $=\frac{20}{5}=4$
$\Rightarrow \frac{N}{N_0}={\left[\frac{1}{2}\right]}^{}={\left[\frac{1}{2}\right]}^4$
$\Rightarrow \frac{N}{N_0}=\frac{1}{16}$
$N=\frac{N_0}{16}$
Disintegrated $y\Rightarrow \left[\frac{N_0-N}{N_0}\right]\times 100=[1-\frac{N}{N_0}]\times 100$
$\Rightarrow [1-\frac{1}{16}]\times 100=93.75$%