Question

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

• A. zero
• B. $0.125kg$
• C. $0.5kg$
• D. $0.25kg$

Answer 1

Answer: (B)

From Rutherford and Soddy law for radioactive decay, if $N$ be the number of atonıs of radioactive substance lift at some instant of time, then
$N=N_0{\left(\frac{1}{2}\right)}^n$
where $N_0$ is original number of atoms and $n$ is number of half-lives.
Given, $T_{1/2}=1600$ years,
$N_0=1kg$
$n=\frac{4800}{1600}=3$
$\therefore N={\left(\frac{1}{2}\right)}^3\times 1$
$=\frac{1}{8}\times 1=0.125kg$
Note : The number of atoms of a radioactive substance that is, the radioactive activity of the substance continuously decreases with time.