When the operating potential in an X-ray tube is raised by 1 % , by what percentage will the cutoff wavelength decrease?

Step-by-step solution

The cutoff wavelength of X-rays produced in an X-ray tube is given by the relation: _ c = hc eV Taking the natural logarithm on both sides, we get: _ c = ( hc e ) - V Differentiating the expression for small changes, we obtain: _ c _ c = - V V Multiplying by 100 to get the percentage change: _ c _ c 100 = - ( V V 100 ) Given that the operating potential is raised by 1 % , we have V V 100 = 1 % . _ c _ c 100 = -1 % The negative sign indicates a decrease. Therefore, the cutoff wavelength decreases by 1 % .