Question 566: Atoms & Nuclei

Question

Two radioactive materials X
1
and X
2
have decay constants $$5\lambda $$ and $$\lambda $$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X
1
to that X
2
will be 1/e after a time

Accepted Answer

X
1
=  N
0
e
Ã¢ÂÂ5$$\lambda $$t
X
2
=  N
0
e
Ã¢ÂÂ$$\lambda $$t
Given $${{{X_1}} \over {{X_2}}}$$ = $${1 \over e}$$
$$ \Rightarrow $$ $${{{N_0}{e^{ - 5\lambda t}}} \over {{N_0}{e^{ - \lambda t}}}}$$ = $${1 \over e}$$
$$ \Rightarrow $$ e
Ã¢ÂÂ4$$\lambda $$t
= e
-1
$$ \Rightarrow $$ t = $${1 \over {4\lambda }}$$

Answer

1/4$$\lambda $$

Answer

e/$$\lambda $$

Answer

$$\lambda $$

Answer

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

Atoms & Nuclei

Two radioactive materials X 1 and X 2 have decay constants $5\lambda and \lambda $ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X 1 to that X 2 will be 1/e after a time

Choose the correct answer: