Question 276: Atoms & Nuclei

Question

Two radioactive substances A and B have decay constants 5$$\lambda $$ and $$\lambda $$ respectively. At t = 0, a sample has the
same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $${\left( {{1 \over e}} \right)^2}$$
 will be :

Accepted Answer

N
x
(at t) = N
0
e
Ã¢ÂÂ5$$\lambda $$t
N
y
(at t) = N
0
e
Ã¢ÂÂ$$\lambda $$t
$${{{N_x}} \over {{N_y}}} = {1 \over {{e^2}}} = {e^{ - 4\lambda t}}$$
$$ \Rightarrow 4\lambda t = 2$$
$$ \Rightarrow t = {2 \over {4\lambda }} = \left( {{1 \over {2\lambda }}} \right)$$

Answer

$${2 \over \lambda }$$

Answer

$${1 \over {4\lambda }}$$

Answer

$${1 \over {2\lambda }}$$

Answer

$${1 \over {\lambda }}$$

Atoms & Nuclei

Two radioactive substances A and B have decay constants 5$\lambda and \lambda respectively. At t = 0, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become {\left( {{1 \over e}} \right)^2}$ will be :

Choose the correct answer: