Question

The half-life of 215 At is 100 $\mu s$. The time taken for the radioactivity of a sample of 215 At to decay to $\frac{1}{{16}^{th}}$ of its initial value is

• A. $400\mu s$
  
• B. $6.3\mu s$
  
• C. $40\mu s$
  
• D. $300\mu s$

Answer 1

The correct option is A $400\mu s$


By using $N=N_0{\left(\frac{1}{2}\right)}^n\Rightarrow \frac{N}{N_0}={\left(\frac{1}{2}\right)}^{t{T}_{Half}}\Rightarrow \frac{1}{16}={\frac{1}{2}}^{\frac{t}{100}}\Rightarrow t=400\mu sec$.