Question

The activity of a radioactive sample falls from $700\, s^{-1}$ to $500\, s^{-1}$ in 30 minutes. Its half life is close to :

• A. $72$ min
• B. $62$ min
• C. $66$ min
• D. $52$ min

Answer 1

Answer: (B)

$62$ min

Answer 2

$A = A_{0} \left(\frac{1}{2}\right) \frac{t}{T_{1/ 2}}$
$500 = 700 \left(\frac{1}{2}\right) \frac{t}{T_{1/ 2}}$
$0.7 \approx \left(\frac{1}{2}\right) \frac{t}{T_{1/ 2}}$
$\left(\frac{1}{2}\right)^{_{1/ 2}}\approx \frac{t}{T_{1/ 2}}$
$\frac{30}{T_{_{1/ 2}}} \approx \frac{1}{2} \Rightarrow T_{_{1/ 2}} = 60$