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A radioactive specimen shows a disintegration rate of 5000 counts per minute at a given instant. Five minutes later, its disintegration rate falls to 1250 counts per minute. The decay constant (per minute) is

1. 0.4 ln 2
2. 0.2 ln 2
3. 0.1 ln 2
4. 0.8 ln 2

Correct answer: 0.4 ln 2

Solution

The decay constant is calculated using the formula for exponential decay, which relates the initial and final counts over time. In this case, the counts decrease from 5000 to 1250 in 5 minutes, indicating a decay factor that can be expressed in terms of the decay constant, leading to the correct option of 0.4 ln 2.

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