Question

A radioactive substance has a half-life of 1 year. The fraction of this material, that would remain after 5 years will be.

• A. $\frac{1}{32}$
• B. $\frac{1}{5}$
• C. $\frac{1}{2}$
• D. $\frac{4}{5}$

Answer 1

Answer: (A)

$\frac{1}{32}$

Answer 2

Number of half lives $n = \frac{5}{1} = 5$

Now $\frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{n} \Rightarrow \frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{5} = \frac{1}{32}$.