First slide

Radio activity

Question

For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is

Moderate

A

20
B

10
C

30
D

15

Solution

Number of nuclei remaining
N=600-450=150
According to the law of radioactive decay,
$\frac{N}{N_{0}} = {(\frac{1}{2})}^{\frac{t}{T_{1 / 2}}}; where N_{0} is the number of nuclei initially.$
$∴ \frac{150}{600} = {(\frac{1}{2})}^{\frac{t}{T_{1 / 2}}}; where T_{1 / 2} = half life.$
$or {(\frac{1}{2})}^{2} = {(\frac{1}{2})}^{\frac{t}{T_{1 / 2}}} \Rightarrow t = 2 T_{1 / 2} = 2 \times 10 minutes = 20 m i n u t e s$

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