Question 290: Atoms & Nuclei

Question

At some instant,  a radioactive sample S1 having an activity 5 $$\mu $$Ci has twice the number of nuclei as another sample S2 which has an activity of 10 $$\mu $$Ci. The half lives of S1 and S2 are :

Accepted Answer

As per question, N
1
= 2N
2
Also A
1
= 5 $$\mu $$Ci, A
2
= 10 $$\mu $$Ci
As A = $$\lambda $$N = $${{\ln 2} \over {{T_{1/2}}}}N$$
$$ 	herefore $$ $${{{A_1}} \over {{A_2}}} = {{{{\left( {{T_{1/2}}} ight)}_2}} \over {{{\left( {{T_{1/2}}} ight)}_1}}} 	imes {{{N_1}} \over {{N_2}}}$$
$$ \Rightarrow $$ $${{{{\left( {{T_{1/2}}} ight)}_1}} \over {{{\left( {{T_{1/2}}} ight)}_2}}} = {{{N_1}} \over {{N_2}}} 	imes {{{A_2}} \over {{A_1}}}$$ = 2 $$ 	imes $$ 2 = 4
So half life of sample S
1
should be four timrs than sample S
2
.

Answer

20 years and 5 years,  respectively

Answer

20 years and 10years,  respectively

Answer

5 years and 20 years, respectively

Answer

10 years and 20 years,  respectively

Atoms & Nuclei

At some instant, a radioactive sample S1 having an activity 5 $\mu Ci has twice the number of nuclei as another sample S2 which has an activity of 10 \mu $Ci. The half lives of S1 and S2 are :

Choose the correct answer: