The Hydrogen Atom and Rydberg Transitions

When electrons fall from excited states to lower energy levels, photons are emitted.

`stackrel(~)nu=R_H(1/n_1^2 - 1/n_2^2)`
where `n_2>n_1` and `R_H` is the Rydberg Constant

`E_n=-(hcR_H)/n^2`

These energies are negative because work has to be done to promote the electrons to the vacuum. For ionisation, `n_2=oo`, since `1/oo=0`, then

`E_("ionisation")=hcR_H`

diagram

`F=zq^2/(4piepsilon_0r^2`

`V=int_oo^r (zq^2)/(4piepsilon_0r^2)dr=-zq^2/(4piepsilon_0r)`

Hydrogen Spectral Lines

Lyman Series (`n'=1`)			Balmer Series (`n'=2`)			Paschen Series (`n'=3`)
n	`lambda` /nm		n	`lambda` /nm		n	`lambda` /nm
2	122		3	656		4	1870
3	103		4	486		5	1280
4	97.2		5	434		6	1090
5	94.9		6	410		7	1000
6	93.7		7	397		8	954
`oo`	91.1		`oo`	365		`oo`	820

Brackett Series (`n'=4`)			Pfund Series (`n'=5`)
n	`lambda` /nm		n	`lambda` /nm
5	4050		6	7460
6	2920		7	4650
7	2170		8	3740
8	1940		9	3300
9	1820		10	3040
`oo`	1460		`oo`	2280