Question

Half-life of radium is 1600 yr. If the initial mass is 1 kg, what is the amount of radium left after 4800 yr?

• A. Zero
• B. 0.125 kg
• C. 0.5 kg
• D. 0.25 kg

Answer 1

The correct option is B 0.125 kg

From Rutharford and Soddy law for radioactive decay, if N be the number of atoms of radioactive substances lift at some instant of time, then

$N=N_0{\left(\frac{1}{2}\right)}^n$

When $N_0$ is original number of atoms and $n$ is number of half views

Given, $T_1/2=1600yr,N_0=1kg$

$n=\frac{4800}{1600}=3$

$N={\left(\frac{1}{2}\right)}^3\times 1$

$=\frac{1}{8}=0.125kg$