Question 205: Atoms & Nuclei

Question

A radioactive sample is undergoing $$\alpha$$ decay. At any time t
1
, its activity is A and another time t
2
, the activity is $${A \over 5}$$. What is the average life time for the sample?

Accepted Answer

Let initial activity be A
0
A = A
0
e
$$-$$$$\lambda$$t
1
........(i)
$${A \over 5}$$ = A
0
e
$$-$$$$\lambda$$t
2
.......(ii)
(i) $$ \div $$ (ii)
5 = e
$$\lambda$$(t
2
$$-$$ t
1
)
$$\lambda$$ = $${{\ln 5} \over {{t_2} - {t_1}}} = {1 \over 	au }$$
$$	au  = {{{t_2} - {t_1}} \over {\ln 5}}$$

Answer

$${{\ln 5} \over {{t_2} - {t_1}}}$$

Answer

$${{\ln ({t_2} + {t_1})} \over 2}$$

Answer

$${{{t_1} - {t_2}} \over {\ln 5}}$$

Answer

$${{{t_2} - {t_1}} \over {\ln 5}}$$

Atoms & Nuclei

A radioactive sample is undergoing $\alpha decay. At any time t 1 , its activity is A and another time t 2 , the activity is {A \over 5}$. What is the average life time for the sample?

Choose the correct answer: