Electronic Structure

Name	Symbol	Unit
speed of light	$c = 2.9979\times 10^8\frac{m}{s}$	$\frac{m}{s}$
wavelength	$\lambda$	$m$
de Brogli Wavelength (particle wavelength)	$\lambda _{dB}$	$m$
frequency	$v$	$Hz$
Planck's constant	$h=6.62606957\times 10^{-34}Js$	$Js$
work function	$\Phi$	$J$ / $\frac{kJ}{mol}$
threshold frequency, light above this frequency can eject electron from this metal	$v_{thres}$	$Hz$
Rydberg constant	$R_H=1.0974\times 10^7 m^{-1}$	$m^{-1}$
Rydberg energy	$hcR_H=R_E=2.1799\times 10^{-18}$	$J$
principal quantum number	$n$	-
angular momentum quantum number	$l = 0,1,2,...,n-1$	-
magnetic quantum number	$m_l=-l,-l+1,...,l-1,l$	-
spin quantum number	$m_s=\frac{1}{2}$ or $-\frac{1}{2}$	-
atomic number, # of the atom in the periodic table	$Z$	-

Equation	Explain
$c=\lambda v$
$E_{photon}=hv$	$E_{photon}$: energy of a single photon
$E_{photon}=\frac{1}{2}mu^2+\Phi_{metal}$	$m$: mass of the ejected electron ($9.10938356\times 10^{-31}kg$) $u$: speed of the ejected electron
$v_{thres}=\frac{\Phi_{metal}}{h}$
$E_n=-\frac{Z^2hcR_H}{n^2}$	$n=1,2,3.....$ $E_n$: energy of energy level $n$
$\Delta E=Z^2hcR_H(\frac{1}{n^2}-\frac{1}{n'^2})$	$n'>n$ $\Delta E$: energy needed to transition to another energy level
$\lambda = \frac{c}{v}=\frac{1}{Z^2R_H(\frac{1}{n^2}-\frac{1}{n'^2})}$	$n'>n$ $\lambda$: wavelength of light needed to transition to another energy level
$\lambda_{dB}=\frac{h}{mu}$

A pair of ($n$, $l$, $m_l$) uniquely identifies an orbital, each orbital has two states ($m_s$)

Subshells are labeled by $n$ and $l$, $l$ value is represented by a letter: s=0, p=1, d=2, f=3, g=4

---

Pauli exclusion principle: two electrons with the same spin cannot occupy the same orbital

Hund's rule: In general, electrons with the same $n$ and $l$ values spread out into different orbitals, as much as possible, with the same spin, as much as possible.

Aufbau principle: In ground state, the orbitals are filled from the bottom to the top ($n$ and $l$), left to right($m_l$). (each square in the image can hold two electrons of different $m_s$​) (the orbital at the bottom has the lowest energy):

Two exceptions to the Aufbau principle in the first 40 elements:

Name	Electron Configuration	Noble Gas Shorthand Notation
Chromium (Cr)	1s22s22p63s23p64s13d5	[Ar] 4s13d5
Copper (Cu)	1s22s22p63s23p64s13d10	[Ar] 4s13d10

Magnetic Response

Atoms with unfilled subshell are paramagnetic, meaning them are drawn into a magnetic field

Atoms with no unfilled subshell are diamagnetic, meaning them are slightly repelled from a magnetic field

---

Last update: October 14, 2021
Created: September 19, 2021