Question

At a given instant there are 25% undecayed radio-active nuclei in a sample. After 10 seconds the number of undecayed nuclei reduces to 12.5%. Calculate (i) mean-life of the nuclei, and (ii) the time in which the number of undecayed nuclei will further reduce to 6.25% of the reduced number.

Answer 1

Given: Radio active sample goes $25$% to $12.5$% in $10$ Sec

Half life of the radioactive nuclei is $10$ s

$t_{1/2}=10$ s

a) Mean life of the nuclei is

$\tau =\frac{t_{1/2}}{0.693}=14.43$ s

b) From $12.5\%$ the nuclei has to reduce to $6.25\%$ at this value

$N=No{\left(\frac{1}{2}\right)}^n$

${\left(\frac{1}{2}\right)}^n=\frac{6.25}{100}$

$2^n=16\Rightarrow n=4$

Hence in $4$ half live

So, time taken to

do so $=10\times 4$

$=40$s