Rydberg's Equation

Furthermore, if light is absorbed or emitted by electrons which jump from orbit to orbit, then the energy difference between the orbits should be related (equal to) the energy of the photons that get absorbed! It is:

$$E = \left( \frac{Rhc}{n^2} - \frac{Rhc}{m^2} \right)$$ (6)

The left side is the energy of a photon of light. The right side is the energy difference (via Rydberg's constant, $R=1.097\times 10^{7}\mbox{$\phantom{1\!}^{{\rm 1}\!\!}/_{\!\!{\rm m}}$ }$, h, and the speed of light, $c=3.00\times 10^{8}\mbox{$\phantom{1\!}^{{\rm m}\!\!}/_{\!\!{\rm s}}$ }$) between the orbits. The wavelength is related to the frequency via $\lambda f = c$, so the energy of the photon can be written

$$E = hf \mbox{\ \ \ \ or\ \ \ \ } E=\frac{hc}{\lambda}$$ (7)

Equation 6 is usually written $\frac{1}{\lambda} = R \left( \frac{1}{n^2} - \frac{1}{m^2} \right)$.

 

Table 2: This table shows a few representative elements and in which orbits the electrons reside. Notice that most of the atoms have been left out. I included the first five to show the filling order and the rest to show the configuration pattern.

 

electrons	element		electron configuration
1	H	Hydrogen	1S1
2	He	Helium	1S2
3	Li	Lithium	1S2 2S1
4	Be	Beryllium	1S2 2S2
5	B	Boron	1S2 2S22P1
10	Ne	Neon	1S2 2S22P6
12	Mg	Magnesium	1S2 2S22P6 3S2
18	Ar	Argon	1S2 2S22P6 3S23P6
20	Ca	Calcium	1S2 2S22P6 3S23P6 4S2
30	Zn	Zinc	1S2 2S22P6 3S23P6 4S24D10
36	Kr	Krypton	1S2 2S22P6 3S23P6 4S24D104P6