Question 538: Atoms & Nuclei

Question

The half life of a radioactive nucleus is 50 days. The time invertal (t
2
$$-$$ t
1
) between the time t
2
when $${2 \over 3}$$ of it has decayed and the time t
1
when $${1 \over 3}$$ of it had decayed is

Accepted Answer

At time t
2
, $${2 \over 3}$$ of the sample had decayed
$$ 	herefore $$ N = $${1 \over 3}$$N
0
$$ 	herefore $$ $${1 \over 3}$$N
0
= N
0
$${e^{ - \lambda {t_2}}}$$ ......(1)
At time t
1
, $${1 \over 3}$$ of the sample had decayed
$$ 	herefore $$ N = $${2 \over 3}$$N
0
$$ 	herefore $$ $${2 \over 3}$$N
0
= N
0
$${e^{ - \lambda {t_1}}}$$ ......(2)
Divide (i) by (ii), we get
$${1 \over 2} = {{{e^{ - \lambda {t_2}}}} \over {{e^{ - \lambda {t_1}}}}}$$
$$ \Rightarrow $$ $${1 \over 2} = {e^{ - \lambda \left( {{t_2} - {t_1}} ight)}}$$
$$ \Rightarrow $$ $${\lambda \left( {{t_2} - {t_1}} ight)}$$ = ln 2
$$ \Rightarrow $$ $${\left( {{t_2} - {t_1}} ight)}$$ = $${{\ln 2} \over \lambda }$$ = $${{\ln 2} \over {{{\ln 2} \over {{T_{1/2}}}}}}$$ = T
1/2
= 50 days

Answer

30 days

Answer

50 days

Answer

60 days

Answer

15 days

Atoms & Nuclei

The half life of a radioactive nucleus is 50 days. The time invertal (t 2 $- t 1 ) between the time t 2 when {2 \over 3} of it has decayed and the time t 1 when {1 \over 3}$ of it had decayed is

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