A detector placed 0.20 m from a sealed gamma ray source receives a mean count rate of 2550 counts per minute.  The mean background radiation count is 50 counts per minute.  The experiment is set up as shown:

		To counter

 

Calculate the least distance between the source and the detector if the count rate is not to exceed 6000 counts per minute.

Corrected count rate = 2550 – 50 = 2500 min^-1 (P)

Corrected count rate at new position = 6000 – 50 = 5950 min^-1 (P)

Formula:  I = kIo/x²

2500 = kIo/0.2² and 5950 = kIo/x²  k is the same in both and Io is the same. (P)

Rearranging: 2500 × 0.04 = kIo = 5950 × x²

x² = 2500 × 0.04 = 0.0168 m² (P)

        5950 

x = 0.13 m (P)