When the operating voltage of an X-ray tube is raised to 1.5 times its initial value, the short-wavelength limit undergoes a shift of 26 pm . Determine the initial operating voltage.

Step-by-step solution

The short-wavelength limit of an X-ray tube is given by = hc eV . Let the initial operating voltage be V . The initial short-wavelength limit is ₁ = hc eV . When the voltage is increased to 1.5 V , the new short-wavelength limit becomes ₂ = hc 1.5 eV = 2 3 ₁ . The shift in the short-wavelength limit is given as 26 pm . Thus, ₁ - ₂ = 26 pm ₁ - 2 3 ₁ = 26 pm 1 3 ₁ = 26 pm ₁ = 78 pm Using the value of hc 1240 eV nm = 1240 10^3 eV pm , the initial voltage V is: V = hc e ₁ = 1240 10^3 eV pm e 78 pm V = 1240000 78 V 1589