Q. After $5$ half-lives, what percentage quantity of a radioactive element remains undecayed?
NTA AbhyasNTA Abhyas 2022
Solution:
Given,
Number of half lives $\left(n\right)=5$
$N\left(\text{remain undecayed}\right)=\frac{N_{0} \left(\text{initial undecayed}\right)}{2^{n}}$
$\frac{N}{N_{0}}=\frac{1}{2^{5}}=\frac{1}{32}\frac{N}{N_{0}}\times 100=\frac{100}{32}=3.125\%$
Number of half lives $\left(n\right)=5$
$N\left(\text{remain undecayed}\right)=\frac{N_{0} \left(\text{initial undecayed}\right)}{2^{n}}$
$\frac{N}{N_{0}}=\frac{1}{2^{5}}=\frac{1}{32}\frac{N}{N_{0}}\times 100=\frac{100}{32}=3.125\%$