Question

Initial number of nuclei of a radioactive substance is $5\times {10}^{16}$ and half-life is $10$ yrs. Find the number of nuclei decayed in $5$ yrs.

• A. $2\times {10}^{16}$
• B. $1.5\times {10}^{16}$
• C. $3.5\times {10}^{16}$
• D. $2.5\times {10}^{16}$

Answer 1

The correct option is B $1.5\times {10}^{16}$

$Remaining$ nuclei after $5$ years will be $N=5\times {10}^{16}\times (\frac{1}{2}{)}^{5/10}=\frac{5\times {10}^{16}}{\sqrt[2]{22}}=\frac{5\times {10}^{16}}{1.414}=3.54\times {10}^{16}$

So the decayed nuclei will be $(5-3.54)\times {10}^{16}=1.46\times {10}^{16}$

nearly $1.5\times {10}^{16}$