Question

what is the half life of a radioactive substance if 87.5% of any given amount of the substance disintegrate in 40 minutes​

Answer 1

All radioactive decay reactions follow first order kinetics

Answer 2

Answer: 13.86 minutes

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 = time of decomposition = 40 minutes

a = let initial amount of the reactant  = 100g

a - x = amount left after decay process = (100-87.5)g = 12.5g

$40=\frac{2.303}{k}\log\frac{100}{12.5}$

$k=0.05min^{-1}$  

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

$t_{\frac{1}{2}}=\frac{0.693}{k}$

$t_{\frac{1}{2}}=\frac{0.693}{0.05}=13.86min$

Thus half life of a radioactive substance is 13.86 minutes.