Solveeit Logo

Question

Question: If T is the half life of a radioactive material, then the fraction that would remain after a time \(...

If T is the half life of a radioactive material, then the fraction that would remain after a time T2\frac{T}{2} is.

A

12\frac{1}{2}

B

34\frac{3}{4}

C

12\frac{1}{\sqrt{2}}

D

212\frac{\sqrt{2} - 1}{\sqrt{2}}

Answer

12\frac{1}{\sqrt{2}}

Explanation

Solution

Fraction remains after n half lives

NN0=(12)n=(12)t/T\frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{n} = \left( \frac{1}{2} \right)^{t/T}

NN0=(12)T/2T=(12)1/2=12\frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{\frac{T/2}{T}} = \left( \frac{1}{2} \right)^{1/2} = \frac{1}{\sqrt{2}}.