Question

Strontium−90 is one of the products of the fission of uranium−235. This strontium isotope is radioactive, with a half-life of 28.1 yr. Calculate how long (in yr) it will take for 1.00 g of the isotope to be reduced to 0.600 g by decay.

Answer 1

Answer : The time passed in years is 20.7 years.

Explanation :

Half-life = 28.1 years

First we have to calculate the rate constant, we use the formula :

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

$k=\frac{0.693}{28.1\text{ years}}$

$k=2.47\times 10^{-2}\text{ years}^{-1}$

Now we have to calculate the time passed.

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  = $2.47\times 10^{-2}\text{ years}^{-1}$

t = time passed by the sample  = ?

a = initial amount of the reactant  = 1.00 g

a - x = amount left after decay process = 0.600 g

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

$t=\frac{2.303}{2.47\times 10^{-2}}\log\frac{1.00}{0.600}$

$t=20.7\text{ years}$

Therefore, the time passed in years is 20.7 years.