The percentage of the original nuclei of the sample of a radioactive substance left after 5 half-lives is?

A. 8%
B. 5%
C. 3%
D. 1%

Correct Answer:

Option C = 3%

Explanation

After 5 half-lives, the fraction of any radio-active substance left = (¹/₂)⁵ = ¹/₃₂
Thus the percentage of the original nuclie = ^1/32/₁ x ¹⁰⁰/₁
assuming the original amount is unity percentage left
= ¹/₃₂ x ¹⁴⁰⁰/₁ = 3.12