Question

After 3 hours, only 0.25 mg of a pure radioactive material is left, if initial mass was 2 mg then the half life of the substance is :

• A. 1.5 hr
• B. 1 hr
• C. 2.5 hr
• D. 2 hr

Answer 1

The correct option is B 1 hr

Man of the substance is proportional to no of nuclei (N) we can use, at time $t$

$N=N_0{\left(\frac{1}{2}\right)}^{t/T}$ [T: Half life period]

at time $t=3hr,N=0.25mg$ from $N_0=2mg$

$0.25=2{\left(\frac{1}{2}\right)}^{t/T}$

$={\left(\frac{1}{2}\right)}^{3/T}=\frac{0.25}{2}=\frac{1}{8}$

$=\frac{3}{T}=3$

$=T=1hr$