Two radioactive elements $E_1$ and $E_2$ with their half lives $T_1$ and $T_2$ have undecayed atoms $n_1$ and $n_2$ respectively present at a given instant. What will be the ratio of their activities at this instant?

$n_1 T_2: n_2 T_1$

The correct answer is Option (3) → $n_1 T_2: n_2 T_1$

The decay constant (λ) is related to its half life $(T_{1/2})$ by -

$λ=\frac{ln2}{T_{1/2}}$

Activity of element $E_1$

$A_1=λn_1=\frac{ln2}{T_1}n_1$

Activity of element $E_2$

$A_2=λ_2n_2=\frac{ln2}{T_2}n_2$

$∴\frac{A_1}{A_2}=\frac{n_1T_2}{n_2T_1}$