Question

A pure radioactive substance has a mass of 30 micrograms but had a mass of 240 micrograms 48 years ago. Assuming that the only changes in mass are due to radioactive decay, the half-life of the substance is _______ years. Please choose the correct answer from the following choices, and then select the submit answer button.

Answer 1

Answer: Half-life of the substance is 16 years.

Explanation:

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant  

t = age of sample  = 48 years

a = initial amount of the reactant = 240 micrograms

a - x = amount left after decay process = 30 microgarms

$48=\frac{2.303}{k}\log\frac{240}{30}$

$k=\frac{2.303}{48}\log\frac{240}{30}$

$k=0.0433years^{-1}$

b) $t_{\frac{1}{2}}$ of reaction  

$t_{\frac{1}{2}}=\frac{0.693}{k}=\frac{0.693}{0.0433}=16years$

Thus half-life of the substance is 16 years.