Cheat Sheet: PC-02 Atomic Structure — One-Page Revision — Notes

Constants

h	c	R_H	mₑ	1 eV
$6.626 \times 10^{-34}$ J·s	$3 \times 10^{8}$ m/s	$1.097 \times 10^{7}$ $m^{-1}$	$9.1 \times 10^{-31}$ kg	$1.6 \times 10^{-1}$ ^{9} J

Master Formulas

$E_n = -\frac{13.6 Z^2}{n^2} \text{ eV} \quad r_n = \frac{0.529 n^2}{Z} \text{ Å} \quad v_n = \frac{2.18 \times 10^6 Z}{n} \text{ m/s}$ $\frac{1}{\lambda} = R_H Z^2\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right) \quad \lambda = \frac{h}{mv} \quad KE = h(\nu - \nu_0) \quad \Delta x \cdot \Delta p \geq \frac{h}{4\pi}$

Spectral Series

Series	n_{1}	Region	First Line
Lyman	1	UV	121.6 nm
Balmer	2	Visible	656.3 nm
Paschen	3	IR	1875 nm
Brackett	4	IR	4051 nm
Pfund	5	Far IR	7460 nm

Nodes: n=3 Examples

Orbital	Total	Angular	Radial
3s	2	0	2
3p	2	1	1
3d	2	2	0

Anomalous Configurations

Cr (Z=24): [Ar] 3 $d^{5}$ 4 $s^{1}$ (half-filled $d^{5}$ stability)
Cu (Z=29): [Ar] 3 $d^{10}$ 4 $s^{1}$ (fully-filled $d^{10}$ stability)

Orbital Capacities

Subshell	l	Orbitals	Max $e^{-}$
s	0	1	2
p	1	3	6
d	2	5	10
f	3	7	14

Lines from Level n: n(n−1)/2

n=2:1, n=3:3, n=4:6, n=5:10, n=6:15

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Cheat Sheet: PC-02 Atomic Structure — One-Page Revision