Question

At a given instant, there are 50% undecayed
radioactive nuclei. After another 40 s, the number of
undecayed nuclei reduces to 3.125 %. The mean life
of radioactive element is
(1) 14.4 s
(2) 7.21 s
(3) 28.8 s
4)10s

Answer 1

Answer:

The average life is 14.4 s.

Explanation:

The half life is the time for 50% decay and it is related to decay constant as:

$t_{\frac{1}{2}=\frac{0.693}{k}$

Where

k = decay constant

The mean life is related to decay constant as:

$meanlife=\frac{1}{k}$

Let initial concentration of the nuclei is A₀

The concentration or amount initially is $\frac{A_{0}}{2}$

the amount left after 40 seconds is = 0.03125A₀

Let us calculate the rate or decay constant from this as:

$kt=ln(\frac{[A_{0}]}{[A_{t}]} )$

time = 40 seconds

putting values

$k(40)=ln(\frac{[0.5A_{0}]}{[0.03125[[A_{0}]} )$

k=0.0693$meanlife=\frac{1}{k}=\frac{1}{0.0693}= 14.4s$