In the last part of the experiment you need to investigate the behaviour of gamma radiation as it passes through air. a gamma source is placed at a distance d = 0.064 m away from the gm detector and the counts per minute recorded c = 585.

as we expect gamma radiation not to be absorbed by air an inverse square law type behaviour should be seen, where the count rate will decrease with distance. to see if this is correct you need to plot a graph, with data collected at different distances. looking at the data given above, what point would you plot on the x-axis?

linear cart C Vs 1/R²  or log cart C Vs R

Explanation:

Gamma radiation is very high energy electromagnetic rays, but its behavior is the same as for all radiation. By the principle of conservation of energy after the radiation is emitted, it must be distributed on a spherical surface which determines the behavior of the inverse of the square.

In this experiment you are measuring the rate of counts by time (C), this must be the dependent variable since it is not controlled by the experimenter and on the other hand it measures the distance (X) this is the independent variable since it is the one that we can control.

To make a graph with this data, the counting rate must be plotted against the inverse of the squared distance (1/R²). On the Y axis the counts per second and the X 1 / R² axis, with this graph a line must be obtained.

Another graph that we can make on double logarithmic paper where the Y axis plotted the counting rate and on the X axis the distance, the slope should give -2.

            C == A / R²

        Log C = log A -2 log R

With either of the two graphs, the law of the inverse of the square is tested

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .