Question

The half life of $B{i}^{210}$ is 5 days. What time is taken by $(7/8{)}^{th}$ part of the sample to decay?

• A. 3.4 days
• B. 10 days
• C. 15 days
• D. 20 days

Answer 1

Answer: (C)

$N=N_0{\left[\frac{1}{2}\right]}^{1/T}$
$N=\left(1-\frac{7}{8}\right)N_0$
$\frac{N_0}{8}=N_0{\left[\frac{1}{2}\right]}^{1/5}$
${\left(\frac{1}{2}\right)}^3={\left[\frac{1}{2}\right]}^{1/5}$
$\Rightarrow t=15$ days.