Question

After $5$ half-lives, what percentage quantity of a radioactive element remains undecayed?

• A. $4.125\%$
• B. $3.125\%$
• C. $31.1\%$
• D. $42.125\%$

Answer 1

Answer: (B)

Given,
Number of half lives $\left(n\right)=5$
$N\left(\text{remain undecayed}\right)=\frac{N_0\left(\text{initial undecayed}\right)}{2^n}$
$\frac{N}{N_0}=\frac{1}{2^5}=\frac{1}{32}\frac{N}{N_0}\times 100=\frac{100}{32}=3.125\%$