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.

43.73 seconds

Explanation:

Half-life of indium = 14.10 sec

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

Now we have to calculate the age of the sample:

Expression for rate law for first order kinetics is given by:

where,

k = rate constant  

t = age of sample = ?

a = initial amount of the reactant = 7.70 mg=  

a - x = amount left after decay process =

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

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