Question:
The count rate of a Geiger Muller counter for the radiation of a radioactive material of half-life of 30 minutes decreases to 5 second$^{-1}$ after 2 hours. The initial count rate was
The count rate of a Geiger Muller counter for the radiation of a radioactive material of half-life of 30 minutes decreases to 5 second$^{-1}$ after 2 hours. The initial count rate was
Updated On: Jul 13, 2024
- 80 second$^{-1}$
- 625second $^{-1}$
- 20second $^{-1}$
- 25 second $^{-1}$
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The Correct Option is A
Solution and Explanation
Half-life time = 30 minutes; Rate of decrease
(N) = 5 per second and total time = 2 hours = 120 minutes.
Relation for initial and final count rate
$\frac{N}{N_0}=\bigg(\frac{1}{2}\bigg)^{time/half-life} =\bigg(\frac{1}{2}\bigg)^{120/30}=\bigg(\frac{1}{2}\bigg)^4=\frac{1}{16}.$
Therefore N$_0$= 16 x N = 16 x 5 = 80 $s^{-1}$
(N) = 5 per second and total time = 2 hours = 120 minutes.
Relation for initial and final count rate
$\frac{N}{N_0}=\bigg(\frac{1}{2}\bigg)^{time/half-life} =\bigg(\frac{1}{2}\bigg)^{120/30}=\bigg(\frac{1}{2}\bigg)^4=\frac{1}{16}.$
Therefore N$_0$= 16 x N = 16 x 5 = 80 $s^{-1}$
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Concepts Used:
Decay Rate
The disintegration of unstable heavy atomic nuclei into lighter, more stable, atomic nuclei, accompanied in the process by the emission of ionizing radiation (alpha particles, beta particles or gamma rays). This is a random process at the atomic level but, given a large number of similar atoms, the decay rate on average is predictable, and is usually measured by the half-life of the substance.
The equation for finding out the decay rate is given below:
