First slide

Radio activity

Question

The half-life of ${Bi}^{210}$ is 5 days. What time is taken by ${(\frac{7}{8})}^{th}$ part of the sample of decay?

Moderate

A

3.4 days
B

10 days
C

15 days
D

20 days

Solution

By using
$N = N_{0} {(\frac{1}{2})}^{t / T}; Where N = (1 - \frac{7}{8}) N_{0} = \frac{1}{8} N_{0} So \frac{1}{8} N_{0} = N_{0} {(\frac{1}{2})}^{t / T} \Rightarrow {(\frac{1}{2})}^{3} = {(\frac{1}{2})}^{t / 5} \Rightarrow t = 15 days$

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