For a certain material, the wavelengths of the K_ and L_ X-rays are given as 21.3 pm and 141 pm , respectively. Determine the wavelength of the K_ X-ray for this material.

Step-by-step solution

The energy of an X-ray photon is related to its wavelength by E = hc . The transitions corresponding to the given X-rays are: K_ transition: L shell to K shell ( E_ K = E_L - E_K ) L_ transition: M shell to L shell ( E_ L = E_M - E_L ) K_ transition: M shell to K shell ( E_ K = E_M - E_K ) From the energy levels: E_ K = E_ K + E_ L Substituting the energy-wavelength relation: hc _ K = hc _ K + hc _ L 1 _ K = 1 _ K + 1 _ L Given _ K = 21.3 pm and _ L = 141 pm : 1 _ K = 1 21.3 + 1 141 _ K = 21.3 141 21.3 + 141 _ K =