Question

Nuclear decay occurs according to first-order kinetics. Cobalt-60 decays with a rate constant of 0.131 years−1. After 5.00 years, a sample has a mass of 0.302 g. What was the original mass of the sample?

Answer 1

Answer : The original mass of the sample was 0.581 grams.

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  = $0.131\text{ years}^{-1}$

t = time passed by the sample = 5.00 years

a = original or initial amount of the reactant  = ?

a - x = amount left after decay process = 0.302 g

Now put all the given values in above equation, we get

$5.00\text{ years}=\frac{2.303}{0.131\text{ years}^{-1}}\log\frac{a}{0.302g}$

$a=0.581g$

Therefore, the original mass of the sample was 0.581 grams.