Question

In artificial radioactivity, $1.414\times {10}^6$ nuclei are disintegrated into ${10}^6$ nuclei in $10min$ . The half-life in minutes must be:

• A. 5
• B. 20
• C. 15
• D. 30
• E. 25

Answer 1

Answer: (A)

From Rutherford-Soddy law $N=N_0{\left(\frac{1}{2}\right)}^n$
$n=\frac{t}{T}$ $\therefore$
${10}^6=1.414\times {10}^6{\left(\frac{1}{2}\right)}^{t/T}$
$\Rightarrow$ $\frac{1000}{1414}={\left(\frac{1}{2}\right)}^{t/T}$
$\Rightarrow$ ${\left(\frac{1}{2}\right)}^2={\left(\frac{10}{12}\right)}^2$
(Approximately) $\Rightarrow$ $n=2$ $\Rightarrow$ $n=\frac{t}{T}=2$
$\Rightarrow$ $T=\frac{10}{2}=5\min$