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The count rate of a Geiger Muller counter for the radiation of radioactive material of half-life 30 minutes decreases to 5 sec⁻¹ after 2 hours. The initial count rate was

1. 20 sec⁻¹
2. 25 sec⁻¹
3. 80 sec⁻¹
4. 625 sec⁻¹

Correct answer: 80 sec⁻¹

Solution

The half-life of the material is 30 minutes, so in 2 hours (120 minutes), 4 half-lives have passed. The count rate decreases by a factor of 2 for each half-life. Thus, the initial count rate is 5 × 2⁴ = 80 sec⁻¹.

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