Question

At radioactive equilibrium, the ratio of two atoms $A$ and $B$ are $3.1\times {10}^9:1$. If half life of '$A$' is $2\times {10}^{10}$ yrs, what is half life of '$B$'?

• A. $6.45$ yrs
• B. $4.65$ yrs
• C. $5.46$ yrs
• D. $5.64$ yrs

Answer 1

Answer: (A)

$6.45$ yrs

Specific radioactivity 'a' is defined as radioconductivity per unit mass at the radionuclide.

Half life is related by equation

$T_{1/2}=\frac{{(N}_A)\ln 2}{a\times m}\therefore \frac{(T_{1/2}{)}_A}{(T_{1/2}{)}_B}=\frac{(N_A{)}_A}{(N_B{)}_B}\frac{2\times {10}^{10}}{(T_{1/2}{)}_B}=3.1\times {10}^9\frac{2.0\times {10}^{10}}{{3.1\times 10}^9}=(T_{1/2}{)}_B{\left(T_{1/2}\right)}_B=6.45years.$