Question

Half-life of a substance is $20$min. then the time between $33$% decay and $67$% decay will be (approx)

• A. $20$ min
• B. $40$ min
• C. $50$ min
• D. $32$ min
• E. None of these

Answer 1

The correct option is A $20$ min

The relation between decay constant $\left(\lambda \right)$ and half-life (T) is:
$\lambda =\frac{log2}{T_{\frac{1}{2}}}=\frac{0.693}{T_{\frac{1}{2}}}=\frac{0.693}{20}=0.03465permin$
Time of decay, $t=\frac{2.303}{\lambda }lo{g}_{10}\frac{N_0}{N}$

Time of decay for $33$% disintegration is:
$t_1=\frac{2.303}{0.03465}lo{g}_{10}\frac{100}{67}=11.6min$

Time of decay for $67$% disintegration is:
$t_2=\frac{1.303}{0.03465}lo{g}_{10}\frac{100}{33}=32min$

Hence, difference of time is :
$\Delta t=t_2-t_1=32-11.6=20.4min\approx 20min$