Hydrogenic Model

As derived in lecture three of the MSE204 Fall 2000 notes, the equation giving the change in energy for an electron transition from state $n_{2}$ to $n_{1}$, of an atom with atomic number, Z, is

$$\Delta E = E_{n_{2}} - E_{n_{1}} = - Er Z \left( \frac{1}{n_{2}^{2}} - \frac{1}{n_{1}^{2}} \right)$$ (1)

Er is the Ryberg energy which is equal to 13.6eV. So for the series K$\alpha$ ($n_{2}=2$, $n_{1}=1$), K$\beta$ ($n_{2}=3$, $n_{1}=1$), and L ($n_{2}=2$, $n_{1}=2$), we express the energy transition as 1. We convert energy to frequency by

$$\nu=\frac{E}{h}$$ (2)

and to wavelength by

$$\lambda=\frac{c}{\nu}$$ (3)

where Planck's constant, h = 4.13566727e-15 eV and the speed of light in vacuum c = 3.0e8 m/s. The results are seen in figure 1.

Figure 1: Results from Hydrogenic Model