Question

A pure radioactive substance has a mass of 30 micrograms but had a mass of 240 micrograms 48 years ago. Assuming that the only changes in mass are due to radioactive decay, the half-life of the substance is _______ years. Please choose the correct answer from the following choices, and then select the submit answer button.

Answer 1

Answer: Half-life of the substance is 16 years.

Step-by-step explanation:

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

`t=(2.303)/(k)\log(a)/(a-x)`

where,

k = rate constant

t = age of sample = 48 years

a = initial amount of the reactant = 240 micrograms

a - x = amount left after decay process = 30 microgarms

`48=(2.303)/(k)\log(240)/(30)`

`k=(2.303)/(48)\log(240)/(30)`

`k=0.0433years^(-1)`

b)
`t_{(1)/(2)}` of reaction

`t_{(1)/(2)}=(0.693)/(k)=(0.693)/(0.0433)=16years`

Thus half-life of the substance is 16 years.