Question

Indium-116 is radioactive and has a half life of 14.10 seconds. How long would it take a sample to decay from 7.70 mg to 900 µg.

Answer 1

Answer: 43.73 seconds

Explanation:

Half-life of indium = 14.10 sec

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

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

$k=\frac{0.693}{14.10}=0.0491sec^{-1}$

Now we have to calculate the age of the sample:

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 = ?

a = initial amount of the reactant = 7.70 mg= $7700\mug$  

 $(1mg=1000\mug$

a - x = amount left after decay process = $900\mug$

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

 $t=\frac{2.303}{0.0491}\log\frac{7700}{900}$

$t=43.73sec$

Thus it would take 43.73 seconds sample to decay from 7.70 mg to 900 µg.