Question

The half-life of radioactive element is $600yr$. The fraction of sample that would remain after $3000yr$ is

• A. 1/2
• B. 1/16
• C. 1/8
• D. 1/32

Answer 1

Answer: (D)

We know that
$n=\frac{1}{T}$
Given, $n=\frac{1}{T}$
$t=3000yr$
$T=600yr$
$n=\frac{3000}{600}=5$
Then, $\frac{N}{N_0}={\left(\frac{1}{2}\right)}^n$
$\frac{N}{N_0}={\left(\frac{1}{2}\right)}^5=\frac{1}{32}$