First slide

Radio activity

Question

What percentage of original radioactive atoms is left after five half-lives?

Moderate

A

0.3 %
B

1 %
C

31 %
D

3.125 %

Solution

Fraction of atoms remains after five half lives
$\frac{N}{N_{0}} = {(\frac{1}{2})}^{t / T} = {(\frac{1}{2})}^{5 T / T} = \frac{1}{32}$
Percentage atom remains $= \frac{1}{32} x 100 = 3.125 %$

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