Question

An important application of exponential functions is working with half-life of radioactive isotopes in chemistry. These isotopes emit particles and decay into stable forms, in doing so they lose mass over time. Half-life of an isotope is the time it takes for the amount to decay by half. For example, the half life of Bromine-85 is 3 minutes. This means if you start with 60g of Br-85, 3 minutes later 30g will remain. How much Br-85 will remain after 20 minutes?

Answer 1

Answer : The amount left after 20 minutes is, 0.592 grams.

Explanation :

Half-life of Bromine-85 = 3 min

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

$k=\frac{0.693}{3\text{ min}}$

$k=0.231\text{ min}^{-1}$

Now we have to calculate the amount left after decay.

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 taken by sample = 20 min

a = initial amount of the reactant  = 60 g

a - x = amount left after decay process  = ?

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

$20=\frac{2.303}{0.231}\log\frac{60}{a-x}$

$a-x=0.592g$

Therefore, the amount left after 20 minutes is, 0.592 grams.