Question 314: Atoms & Nuclei

Question

The half life of a radioactive substance is $$20$$ minutes. The approximate time interval $$\left( {{t_2} - {t_1}} \right)$$ between the time $${{t_2}}$$ when $${2 \over 3}$$ of it had decayed and time $${{t_1}}$$ when $${1 \over 3}$$ of it had decayed is :

Accepted Answer

Number of undecayed atom after time $${t_2};$$
$${{{N_0}} \over 3} = {N_0}{e^{ - \lambda {t_2}}}\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)$$
Number of undecayed atom after time $${t_1};$$
$${{2{N_0}} \over 3} = {N_0}{e^{ - \lambda {t_1}}}\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} \right)$$
From $$(i),$$ $${e^{ - \lambda {t_2}}} = {1 \over 3}$$
$$ \Rightarrow  - \lambda {t_2} = {\log _e}\left( {{1 \over 3}} \right)\,\,\,\,\,\,\,\,...\left( {iii} \right)$$
From $$(ii)$$ $$ - {e^{ - \lambda {t_2}}} = {2 \over 3}$$
$$ \Rightarrow  - \lambda {t_1} = {\log _e}\left( {{2 \over 3}} \right)\,\,\,\,\,\,\,\,\,\,...\left( {iv} \right)$$
Solving $$(iii)$$ and $$(iv),$$ we get
$${t_2} - {t_1} = 20\,$$ min

Answer

$$14$$ min

Answer

$$20$$ min

Answer

$$28$$ min

Answer

$$7$$ min

Atoms & Nuclei

The half life of a radioactive substance is $20 minutes. The approximate time interval \left( {{t_2} - {t_1}} \right) between the time {{t_2}} when {2 \over 3} of it had decayed and time {{t_1}} when {1 \over 3}$ of it had decayed is :

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