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

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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

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