For tungsten, the wavelength of the K_ X-ray is 21.3 pm . Ejecting an electron from the L shell of a tungsten atom requires 11.3 keV . Determine the minimum accelerating voltage across an X-ray tube equipped with a tungsten target that will permit the emission of K_ X-rays.

Step-by-step solution

The energy of the emitted K_ X-ray photon is given by: E_ K_ = hc Using hc 1240 keV pm and = 21.3 pm : E_ K_ = 1240 keV pm 21.3 pm 58.2 keV The K_ X-ray is emitted when an electron transitions from the L shell to a vacancy in the K shell. Therefore, the energy difference between the K and L shells is: E_ K_ = E_K - E_L Given the binding energy of the L shell E_L = 11.3 keV , the binding energy of the K shell is: E_K = E_ K_ + E_L = 58.2 keV + 11.3 keV = 69.5 keV To permit the emission of K_ X-rays, the incident ele