First slide

Radio activity

Question

A radioactive element emits 200 particles per second. After three hours 25 particles per second are emitted. The half-life period of element will be

Moderate

A

50 minutes
B

60 minutes
C

70 minutes
D

80 minutes

Solution

$R = \frac{dN}{dt} \propto N \Rightarrow \frac{R_{2}}{R 1} = \frac{N_{2}}{N_{1}} But \frac{N_{2}}{N_{1}} = {(\frac{1}{2})}^{t / (t_{1} / 2)} \Rightarrow \frac{25}{200} = \frac{1}{8} = {(\frac{1}{2})}^{3} \Rightarrow \frac{t}{t_{1} / 2} = 3 ∴ t_{1} / 2 = \frac{t}{3} = \frac{3}{3} = 1 hour = 60 minutes$

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