Question

A radioisotope has a half - life of 5 years. The fraction of the atoms of the material that would decay in 15 years will be

• A. 1/8
• B. 2/3
• C. 7/8
• D. 1/3

Answer 1

The correct option is C 7/8

Given,

Total time, $T=15years$

Half life, $T_{1/2}=5years$

Hence, number of half life, $n=\frac{15}{5}=3$

We have the formula,

$\frac{N}{N_0}=(\frac{1}{2}{)}^n$

$⟹\frac{N}{N_0}=(\frac{1}{2}{)}^3=\frac{1}{8}$

Hence in $15years$ the $(\frac{1}{8}{)}^{th}$ substance will remain.

Thus, the decayed fraction $=1-\frac{1}{8}=\frac{7}{8}$