Answer
The count rate from a point source typically follows an inverse square law relationship with distance. According to the inverse square law, the intensity of radiation decreases in proportion to the square of the distance from the source.
Mathematically, the count rate (C) is inversely proportional to the square of the distance (D) from the point source. This can be expressed as:
C ∝ 1/D^2
So, if you double the distance from the point source, the count rate would be reduced by a factor of 1/(2^2) or 1/4 of the original count rate. In other words, the count rate would decrease to one-fourth of its initial value.
Note that this relationship assumes ideal conditions and does not account for other factors such as absorption, scattering, or attenuation that may affect the count rate in specific scenarios.