Question

If the half-life of a sample of a radioactive substance is 30 seconds, how much would be left after 60 seconds? A. one-fourth B. half C. one-eighth D. You would need to know how many atoms you are starting with.

Answer 1

$m=m_{0}*(\frac{1}{2})^{\frac{60}{30}}\\\\ m=m_{0}*(\frac{1}{2})^{2}\\\\ m=\frac{1}{4}m_{0}$

If the half-life of a sample of a radioactive substance is 30 seconds, how much would be left after 60 seconds? A. one-fourth

Answer 2

Answer: A. one-fourth

Explanation:

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

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

$k=\frac{0.69}{t_{\frac{1}{2}}}=\frac{0.693}{30}=0.0231$

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  = 60 sec

a = let initial amount of the reactant  = 100 g

a - x = amount left after decay process =

$60=\frac{2.303}{0.0231}\log\frac{100}{a-x}$

$\frac{100}{a-x}=4$

${a-x}=25$

Thus as 25 g of radioactive substance would be left after 60 seconds, which is $\frac{25}{10}=\frac{1}{4}$ of the initial amount.