Question

A radioactive sample contains $10^{-3}kg$ each of two nuclear species $A$ and $B$ with half-life $4days$ and $8days$ respectively. The ratio of the amounts of $A$ and $B$ after a period of $16days$ is

• A. $1:2$
• B. $4:1$
• C. $1:4$
• D. $2:1$
• E. $1:1$

Answer 1

Answer: (C)

Given, half- life of species $A=4$ days
Half- life of species $B=8$ days
For species $A,N=N_0{\left(\frac{1}{2}\right)}^n;n=\frac{16}{4}=4$
Now, $N_1=N_0{\left(\frac{1}{2}\right)}^4$ ...(i)
Similarly, for species $B$
$N_2=N_0{\left(\frac{1}{2}\right)}^2$ ...(ii)
On dividing Eq. (i) from Eq. (ii), we get
$\frac{N_1}{N_2}=\frac{(2{)}^2}{(2{)}^4}$
$\Rightarrow \frac{N_1}{N_2}=\frac{1}{4}$
$\Rightarrow N_1:N_2=1:4$