Question 616: Atoms & Nuclei

Question

Two radioactive substances A and B have decay constants 5$$\lambda $$ and $$\lambda $$ respectively. At t = 0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be (1/e)2 after a time interval

Accepted Answer

N
A
=  N
0
e
Ã¢ÂÂ5$$\lambda $$t
N
B
=  N
0
e
Ã¢ÂÂ$$\lambda $$t
Given $${{{N_A}} \over {{N_B}}}$$ = $${\left( {{1 \over e}} \right)^2}$$
$$ \Rightarrow $$ $${{{N_0}{e^{ - 5\lambda t}}} \over {{N_0}{e^{ - \lambda t}}}}$$ = $${\left( {{1 \over e}} \right)^2}$$
$$ \Rightarrow $$ e
Ã¢ÂÂ4$$\lambda $$t
= e
-2
$$ \Rightarrow $$ t = $${1 \over {2\lambda }}$$

Answer

$$4\lambda $$

Answer

$$2\lambda $$

Answer

1/$$2\lambda $$

Answer

1/$$4\lambda $$

Atoms & Nuclei

Two radioactive substances A and B have decay constants 5$\lambda and \lambda $ respectively. At t = 0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be (1/e)2 after a time interval

Choose the correct answer: