Question

At radioactive equilibrium, the ratio between the atoms of two radioactive elements A and B was found to be $3.1\times {10}^9$: 1 respectively. If $T_{50}$ of the element A is $2\times {10}^{10}$ yrs, then $T_{50}$ of the element B is :

• A. $6.2\times {10}^9$ yr
• B. $6.45$ yr
• C. $2\times {10}^{10}$ yr
• D. $3.1\times {10}^9$ yr

Answer 1

The correct option is B $6.45$ yr

As we know,
$\frac{N_A}{N_B}=\frac{(t_{1/2}{)}_A}{(t_{1/2}{)}_B}$
$3.1\times {10}^9=\frac{2\times {10}^{10}}{(T_{50}{)}_B}$
$(t_{1/2}{)}_B=6.45$ years