Counting Statistics

The net intensity of emitted characteristic X-radiation from an element in a matrix is related to the concentration of that element. Fig. 5.1 illustrates the theoretical correlation between the peak intensity R _P of an element with its concentration C. The true background response R _b is given by the intercept of the curve on the ordinate. The slope m of the curve, sometimes called Fig. 5.1Basis of quantitative X-ray spectrometry. When a plot of peak counting rate (R _p ) against concentration C is made, the slope of the curve is equal to <math display='block'> <mrow> <mfrac> <mrow> <msub> <mi>R</mi> <mi>p</mi> </msub> <mo>&#x2212;</mo><msub> <mi>R</mi> <mi>b</mi> </msub> </mrow> <mi>C</mi> </mfrac> </mrow> </math>$$\frac{{{{R}_{p}}-{{R}_{b}}}}{C}$$ where R _b is the true background counting rate. In practice it is not possible to measure the true R _b and an equivalent background position has to be used away from the analytical line. the calibration factor, is equal to <math display='block'> <mrow> <mfrac> <mrow> <msub> <mi>R</mi> <mi>p</mi> </msub> <mo>&#x2212;</mo><msub> <mi>R</mi> <mi>b</mi> </msub> </mrow> <mi>C</mi> </mfrac> </mrow> </math>$$\frac{{{{R}_{p}}-{{R}_{b}}}}{C}$$ and the concentration is given by (5.1)<math display='block'> <mrow> <mi>C</mi><mo>=</mo><mfrac> <mrow> <msub> <mi>R</mi> <mi>p</mi> </msub> <mo>&#x2212;</mo><msub> <mi>R</mi> <mi>b</mi> </msub> </mrow> <mi>m</mi> </mfrac> </mrow> </math> $$C=\frac{{{{R}_{p}}-{{R}_{b}}}}{m}$$