At a given instant there are 25% undecayed radioactive nuclei in a sample. After 10 s the number of undecayed nuclei reduces to 12.5%. Calculate
(a) mean life of the nuclei,
(b) the time in which the number of undecayed nuclei will further reduce to 6.25% of the reduced number.

Answer

A, C, D

Explanation

(a) In 10 s, number of nuclei has been reduced to half (25% to 12.5%).
Therefore, its half-life is
`t_(1//2) = 10`s
Relation between half-life and mean life is
`t_(mean)=(t_(1//2))/(1n2)=10/0.693s`
`t_(m ean)=14.43s`
(b) From initial 100% to reduction till 6.25%, it takes four half-lives.
`100%overset(t_(1//2))rarr50%overset(t_(1//2))rarr25%overset(t_(1//2))rarr12.5%overset(t_(1//2))rarr6.25%`
`t=4t_(1//2)=4(10)s=40s`
`t=40s`