Question

What is the wavelength of the x-ray emitted from a Tungsten target (Z=74) when an electron moves from the M-shell (n=3) to the K-shell (n=1)

Answer 1

The energy of the electron when it moves from shell $n_1=3$ to $n_2=1$:

$$E=(2.179\cdot10^{-18}\text{ J})Z^2\bigg(\frac{1}{n_2^2}-\frac{1}{n_1^2}\bigg).$$

The wavelength of the x-ray emitted from a Tungsten target is

$$\lambda=\frac{hc}{E}=\frac{hc}{(2.179\cdot10^{-18}\text{ J})Z^2\bigg(\frac{1}{n_2^2}-\frac{1}{n_1^2}\bigg)}=\\\space\\ =444\cdot10^{-6}\text{ m}.$$