Estimation of Error Introduced by Ignoring the Background

Whenever X-ray intensity measurements are made on a selected peak, occuring at a certain setting of the goniometer, some fraction of the measured counting rate is always due to background. The significance of this background is dependent on its relative magnitude, and it is often difficult to judge whether or not it can be ignored in the calculation of the counting error. The true counting error ɛ % is related to the peak R _p and background R _b counting rates in the following way: 6<math display='block'> <mrow> <mi>&#x03B5;</mi><mi>&#x0025;</mi><mo>=</mo><mtext>&#x2009;</mtext><mfrac> <mrow> <mn>100</mn></mrow> <mrow> <msqrt> <mi>T</mi> </msqrt> </mrow> </mfrac> <mo>.</mo><mfrac> <mn>1</mn> <mrow> <msqrt> <mrow> <msub> <mi>R</mi> <mi>p</mi> </msub> </mrow> </msqrt> <mtext>&#x2009;</mtext><mo>&#x2212;</mo><msqrt> <mrow> <msub> <mi>R</mi> <mi>b</mi> </msub> </mrow> </msqrt> </mrow> </mfrac> </mrow> </math>]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$\varepsilon \% = \;\frac{{100}}{{\sqrt T }}.\frac{1}{{\sqrt {{R_p}} \; - \sqrt {{R_b}} }}$$ where T is the total analysis time.