Question

In a radioactive sample, there are $1.414\times 10^{6}$ active nuclei. If they are reduced to $10^{6}$ within $10min$ , then the half life of this sample will be,

• A. $5min$
• B. $20min$
• C. $15min$
• D. $30min$

Answer 1

Answer: (B)

$N=N_{0}\left(\frac{1}{2}\right)^{\left(\frac{t}{T_{\left(1/2\right)}}\right)}$
$\left(10\right)^{6}=1.414\times \left(10\right)^{6}\left(\frac{1}{2}\right)^{\left(\frac{t}{T_{1/2}}\right)}$
$\left(\frac{1}{\sqrt{2}}\right)=\left(\frac{1}{2}\right)^{\left(\frac{t}{T_{1/2}}\right)}$
$\frac{t}{t_{1/2}}=\frac{1}{2}$
$t_{1/2}=2t=20min$ .