When radioactive decay particles are emitted they have equal probability of deca

Question

When radioactive decay particles are emitted they have equal probability of decaying in any direction. If you have a detector of constant area, you will detect more particles the closer you are to the source. As you move further away, you will count fewer, because you are subtending a smaller solid angle of the source. If you increase the source-to-detector distance by a factor of 2.9, what would be the new count rate? Answer in terms of percentage (%) compared with the count rate before you increase the source-to-detector distance.

Explanation / Answer

Let us consider the initial distance between the source and observer is d1
Then the final distance would be = 3.4 d1
We know that Intensity rate = Count Rate /area =
I1 = rate / 4*Pi*d12
Similarly I2 =  rate / 4*Pi*(3.4d1)2
To find the final rate percentage in term of Initial rate
=( Final/intial)*100 = (1/3.42)*100 = 8.65 %

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