Question 199: Atoms & Nuclei

Question

A radioactive sample disintegrates via two independent decay processes having half lives $$T_{1/2}^{(1)}$$ and $$T_{1/2}^{(2)}$$ respectively. The effective half-life T
1/2
of the nuclei is :

Accepted Answer

$${\left( {{{dN} \over {dt}}} ight)_1} = N{\lambda _1},{\left( {{{dN} \over {dt}}} ight)_2} = N{\lambda _2}$$
$${{dN} \over {dt}} = {\left( {{{dN} \over {dt}}} ight)_1} + {\left( {{{dN} \over {dt}}} ight)_2}$$
$$N{\lambda _{eff}} = N{\lambda _1} 	imes N{\lambda _2}$$
$${1 \over {{T_{eff}}}} = {1 \over {{T_1}}} + {1 \over {{T_2}}}$$
$${T_{eff}} = {{{T_1}{T_2}} \over {{T_1} + {T_2}}}$$

Answer

None of the above

Answer

$${T_{1/2}} = T_{1/2}^{(1)} + T_{1/2}^{(2)}$$

Answer

$${T_{1/2}} = {{T_{1/2}^{(1)}T_{1/2}^{(2)}} \over {T_{1/2}^{(1)} + T_{1/2}^{(2)}}}$$

Answer

$${T_{1/2}} = {{T_{1/2}^{(1)} + T_{1/2}^{(2)}} \over {T_{1/2}^{(1)} - T_{1/2}^{(2)}}}$$

Atoms & Nuclei

A radioactive sample disintegrates via two independent decay processes having half lives $T_{1/2}^{(1)} and T_{1/2}^{(2)}$ respectively. The effective half-life T 1/2 of the nuclei is :

Choose the correct answer: