The intensity of radiation from an x-ray source is 900 C/kg at a distance of 20 meters. What will the intensity be at 40 meters?

To determine the intensity of radiation from an x-ray source at a different distance, we can apply the inverse square law of radiation. This law states that the intensity of radiation is inversely proportional to the square of the distance from the source. In mathematical terms, this can be expressed as:

[ I_1/I_2 = (d_2^2)/(d_1^2) ]

where ( I_1 ) and ( I_2 ) are the intensities at distances ( d_1 ) and ( d_2 ), respectively.

In this situation, the initial intensity at 20 meters is 900 C/kg, and we want to find the intensity at 40 meters. By applying the inverse square law:

1. Set ( I_1 = 900 ) C/kg at ( d_1 = 20 ) meters.

2. Let ( I_2 ) be the intensity we want to find at ( d_2 = 40 ) meters.

Plugging in the values:

[ 900 / I_2 = (40^2) / (20^2) ]

Calculating the squares of the distances gives:

[ 40^2 = 160