A student obtain data measuring the range of gammas in lead using thicknesses of

Question

A student obtain data measuring the range of gammas in lead using thicknesses of 0, 3, 6, and 9 cm. For 0 cm thickness, they measure 2742 counts; for 3 cm thickness, they measure 638 counts; for the 6 cm thickness, they record 155 counts; and for 9 cm thickness, they record 26 counts. Next, they plot their results on semilog paper. Along the x-axis they plot x , where x is the thickness. Along the y-axis they plot the number of counts. Because they use semilog paper, this is the same as if they did a linear plot with the y-axis being the logarithm of the number of counts. Then they fit a line through the data, and use the graph to determine the mass absorption coefficient m . On the graph, the mass absorption coefficient is given by


A. The y-intercept of the line (where the line hits the y-axis)
B. The negative of the slope of the line
C. The slope of the line
D. The inverse of the slope of the line
E. The x-intercept of the line (where the extrapolated line hits the x-axis)
F. none of the above

Explanation / Answer

       if N is the number of counts and N_o is the intial number of counts then

                N=N_o*e^-d

                   where is the mass absorption coefficient and d is the thicness

   so log(N/N_o)=-d

                  =log(N/N_o)/d

               from the above relation it is clear that

        the slope of the line gives the absorption coefficient

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