Tables

Table 1 Regions of the Electromagnetic Spectrum. 2

Table 2 Characteristics of Electromagnetic Radiation. 3

Table 3 SI Base Units 4

Table 4 SI Derived Units 5

Table 5 Some Units Commonly Used in Quantum Chemistry. 6

Table 6 Atomic Units 7

Table 7 SI Prefixes 8

Table 8 Physical Constants 8

Table 9 The Greek Alphabet 9

Table 10 Spherical Harmonic Wavefunctions 10

Table 11 Radial Wavefunctions for One-electron Atoms and Ions 12

Table 12 The first eight Hermite polynomials 13

Table 13 Atomic properties 13

Table 14 Atomic configurations 16

Table 15 Real Wavefunctions for One-electron Atomic Orbitals 16

Table 16 Quantum-Mechanical Operators 20

Table 1 Regions of the Electromagnetic Spectrum

Frequency (s^-1)	Energy	Energy (J)	Wavelength
Gamma Rays
>1.0x10¹⁹	>41,000 eV	>6.6x10^-15	<0.03 nm
Hard X-rays
1.2x10¹⁸	5,000 eV	8.0x10^-16	0.25 nm
Soft X-rays
1.2x10¹⁶	50 eV	8.0x10^-18	25 nm
Vacuum UV
1.5x10¹⁵	6.2 eV	9.9x10^-19	200 nm
Ultraviolet
7.5x10¹⁴	25,000 cm^-1	5.0x10^-19	400 nm
Visible
4.3x10¹⁴	14,000 cm^-1	2.8x10^-19	700 nm
Near IR
1.5x10¹⁴	5,000 cm^-1	9.9x10^-20	2.0 μm
Infrared
1.0x10¹³	330 cm^-1	6.6x10^-21	30 μm
Far Infrared
1.0x10¹²	33 cm^-1	6.6x10^-22	300 μm
Microwave
5.0x10⁹	0.17 cm^-1	3.3x10^-24	6.0 cm
Radio Wave

Table 2 Characteristics of Electromagnetic Radiation

ν	frequency of oscillation of the sinusoidal wave
τ = 1/ν	period of oscillation
ω = 2πν	angular frequency of oscillation
c	speed at which a wave front propagates or moves in vacuum
	wavelength
	polarization (a unit vector specifying the direction of the electric field)
E₀	peak amplitude of the electric field
B₀	peak amplitude of the magnetic field, B also is called the magnetic induction
S = E × H	Poynting’s vector, the cross product of the electric and magnetic fields. The units are J/m²s, which gives the amount of energy transported by light per second through a square meter in a direction perpendicular to E and H. H is the magnetic intensity. It also can be called a magnetic field. It is related to the magnetic induction by H = B/μ where μ is the permeability.
I	The intensity or flux of the radiation gives the amount of energy falling on a square meter area per second. It equals in a vacuum and is the average of Poynting’s vector over a period of the electromagnetic wave (ε_o is the permittivity and μ_o is the permeability of a vacuum.).
k	The wave vector has a magnitude of 2π/λ and points in the direction of propagation of the wave.
ε = h ν	Photon energy, where h = Planck's constant.
	wavenumber value, the number of waves or complete cycles per centimeter.

Additional explanation of these quantities will be provided as we encounter them in contexts dealing with atoms and molecules. If you wish to learn more now, see G.R. Fowles, Introduction to Modern Optics (Holt, Rinehart, and Winston, New York, 1968) pp. 1-56 or any book on electromagnetism.

Table 3 SI Ba se Units

Physical Quantity	Name of Unit	Symbol for Unit
mass	kilogram	kg
length	meter	m
time	second	s
temperature	kelvin	K
electric current	ampere	A
amount of substance	mole	mol
luminous intensity*	candela	cd

*The luminous intensity and candela are needed in photometry but seldom in physical chemistry because they result from integrals over all wavelengths that include the spectral distribution of the source and the human visual response. In physical chemistry, we generally are concerned with the response of atoms and molecules to radiation at a single wavelength or narrow band of wavelengths.

Table 4 SI Derived Units

Physical Quantity	Name	Symbol	Definition of Unit
frequency	hertz	Hz	1/s
force	newton	N	m kg/s²
energy	joule	J	m² kg/s² = N m
power	watt	W	J/s
light intensity (also flux)	irradiance	W/m²	J/m²s
pressure	pascal	Pa	N/m²
electric charge	coulomb	C	A s
electric potential difference	volt	V	J/C
electric resistance	ohm	Ω	V/A
electric conductance	siemens	S	1/Ω
electric capacitance	farad	F	C/V
magnetic flux	weber	Wb	V s
inductance	henry	H	V s/A
magnetic flux density	tesla	T	V s/m²

Table 5 Some Units Commonly Used in Quantum Chemistry

Physical Quantity	Name of Unit	Symbol	SI Equivalent
length	Angstrom	Å	10^-10 m = 10^-1 nm
length	micron	μ	10^-6 m
length	Bohr radius	a₀	5.29117 x 10^-11 m
energy	electron volt	eV	1.60218 x 10^-19 J
energy*	wavenumber	cm^-1	1.98645 x 10^-23 J
energy* E = hν	hertz ν	s^-1	6.62608 x 10^-34 J
energy	hartree	H	4.35981 x 10^-18 J
dipole moment	Debye	D	3.33564 x 10^-30 C m
magnetic field	Gauss	G	10^-4 T

*Because they are proportional to energy, wavenumbers and frequency (hertz) commonly are used as units of energy by spectroscopists for convenience.

Table 6 Atomic Units

Physical Quantity	Atomic Unit	SI Equivalent
mass	mass of electron, m_e = 1 au	9.10939 x 10^-31 kg
charge	charge on a proton, e = 1 au	1.60218 x 10^-19 C
length	Bohr radius = a₀ = 1 au	5.29177 x 10^-11 m
energy	1 hartree (E_H) = 1 au	4.35981 x 10^-18 J 27.2114 eV
permittivity	4πε₀ = 1 au	1.11265 x 10^-10 F/m
angular momentum	h/2π = = 1 au	1.05461 x 10^-34 J s

Atomic units often are used by theoreticians to simplify equations and calculations. This simplification results because the units of mass, charge, length, energy, permittivity, and angular momentum are taken to be 1. Of course, to compare the results of calculations with experimental measurements, the atomic units must be converted into SI units. For example, a calculation of energy using atomic units produces a value with the unit hartree. To convert this value to Joules, it must be multiplied by 4.35981 x 10^-18 J/H.

Table 7 SI Pref ixes

Multiple	Prefix	Symbol	Fraction	Prefix	Symbol
10¹⁸	exa	E	10^-1	deci	d
10¹⁵	peta	P	10^-2	centi	c
10¹²	tera	T	10^-3	milli	m
10⁹	giga	G	10^-6	micro	μ
10⁶	mega	M	10^-9	nano	n
10³	kilo	k	10^-12	pico	p
10²	hecto	h	10^-15	femto	f
10	deka	da	10^-18	atto	a

Table 8 Physical Constants

Physical Constant	Symbol	Value
Avogadro constant	N_A	6.02214 x 10²³ mol^-1
Boltzmann constant	k_B	1.38066 x 10^-23 J/K
electron rest mass	m_e	9.10939 x 10^-31 kg
unit of charge*	e	1.60218 x 10^-19 C
Planck constant	h	6.62608 x 10^-34 Js
proton rest mass	m_p	1.67262 x 10^-27 kg
permittivity of free space	ε₀	8.85419 × 10^-12 C²N^-1m^-2
vacuum speed of light	c	2.99792 x 10⁸ m/s

*The fundamental unit of charge has a positive value, is represented by the letter e, and is the magnitude of the charge on a proton (+e) or an electron (-e).

Table 9 The Greek A lphabet

alpha A α	beta B β	gamma Γ γ
delta Δ δ	epsilon E ε	zeta Z ζ
eta H η	theta Θ θ	iota I ι
kappa Κ κ	lambda Λ λ	mu Μ μ
nu Ν ν	xi Ξ ξ	omicron Ο ο
pi Π π	rho Ρ ρ	sigma Σ σ
tau Τ τ	upsilon Υ υ	phi Φ
chi Χ χ	psi Ψ ψ	omega Ω ω

Table 10 Spherical Harmonic Wavefunctions

Atomic Wavefunction Notation

Rotational Wavefunction Notation
m	J	Φ_m()
0	0
0	1
1	1
-1	1
0	2
1	2
-1	2
2	2
-2	2
0	3
1	3
-1	3
2	3
-2	3
3	3
-3	3

Table 11 Radia l Wavefunctions for One-electron Atoms and Ions

n
1	0
2	0
2	1
3	0
3	1
3	2
4	0
4	1
4	2
4	3
5	0

Z is the atomic number of the nucleus, and ρ = Zr/a₀ , where a₀ is the Bohr radius. (See Table 6)

Table 12 The first eight Hermite polynomials

Table 13 Atomic properties

Atomic Symbol	Atomic Number	Radius (10^-9 m)	IP (eV)	IP₂ (eV)	IP₃ (eV)
H	1	0.120	13.598
He	2	0.140	24.587	54.416
Li	3	0.182	5.392	75.638	122.451
Be	4		9.322	18.211	153.893
B	5		8.298	25.154	37.930
C	6	0.170	11.260	24.383	47.887
N	7	0.155	14.534	29.601	47.448
O	8	0.152	13.618	35.116	54.934
F	9	0.147	17.422	34.970	62.707
Ne	10	0.154	21.564	40.962	63.45
Na	11	0.227	5.139	47.286	71.64
Mg	12	0.173	7.646	15.035	80.143
Al	13		5.986	18.828	28.447
Si	14	0.210	8.151	16.345	33.492
P	15	0.180	10.486	19.725	30.18
S	16	0.180	10.360	23.33	34.83
Cl	17	0.175	12.967	23.81	39.61
Ar	18	0.188	17.759	27.629	40.74
K	19	0.275	4.341	31.625	45.72
Ca	20		6.113	11.871	50.908
Sc	21		6.54	12.80	24.76
Ti	22		6.82	13.58	27.491
V	23		6.74	14.65	29.3310
Cr	24		6.766	16.50	30.96
Mn	25		7.435	15.640	33.667
Fe	26		7.870	16.18	30.651
Co	27		7.86	17.06	33.50
Ni	28	0.163	7.635	18.168	35.17
Cu	29	0.143	7.726	20.292	36.83
Zn	30	0.139	9.394	17.964	39.722
Ga	31	0.187	5.999	20.51	30.71
Ge	32		7.899	15.934	34.22
As	33	0.185	9.81	18.633	28.351
Se	34	0.190	9.752	21.19	30.820
Br	35	0.185	11.814	21.8	36
Kr	36	0.202	13.999	24.359	36.95
Rb	37		4.177	27.28	40
Sr	38		5.695	11.030	43.6
Y	39		6.38	12.24	20.52
Zr	40		6.84	13.13	22.99
Nb	41		6.88	14.32	25.04
Mo	42		7.099	16.15	27.16
Tc	43		7.28	15.26	29.54
Ru	44		7.37	16.76	28.47
Rh	45		7.46	18.08	31.06
Pd	46	0.163	8.34	19.43	32.93
Ag	47	0.172	7.576	21.49	34.83
Cd	48	0.158	8.993	16.908	37.48
In	49	0.193	5.786	18.869	28.03
Sn	50	0.217	7.344	14.632	30.502
Sb	51		8.641	16.53	25.3
Te	52	0.206	9.009	18.6	27.96
I	53	0.196	10.451	19.131	33
Xe	54	0.216	12.130	21.21	32.1
Cs	55		3.894	25.1

Ionization potentials from pp. E-63 and E-64 of the CRC Handbook of Chemistry and Physics, 64^th edition, CRC Press, Inc., Boca Raton FL, 1983

Radii are van der Waals radii as reported in p. 164 of Introduction to Coordination, Solid State, and Descriptive Inorganic Chemistry by Glen E. Rodgers, McGraw-Hill, Inc., NY NY, 1994

Table 14 Atomic configurations

Atomic Symbol	Atomic Number	Configuration
H	1	1s¹
He	2	1s²
Li	3	1s² 2s¹
Be	4	1s² 2s²
B	5	1s² 2s² 2p¹
C	6	1s² 2s² 2p²
N	7	1s² 2s² 2p³
O	8	1s² 2s² 2p⁴
F	9	1s² 2s² 2p⁵
Ne	10	1s² 2s² 2p⁶
Na	11	[Ne] 3s¹
Mg	12	[Ne] 3s²
Al	13	[Ne] 3s² 3p¹
Si	14	[Ne] 3s² 3p²
P	15	[Ne] 3s² 3p³
S	16	[Ne] 3s² 3p⁴
Cl	17	[Ne] 3s² 3p⁵
Ar	18	[Ne] 3s² 3p⁶
K	19	[Ar] 4s¹
Ca	20	[Ar] 4s²
Sc	21	[Ar] 3d¹ 4s²
Ti	22	[Ar] 3d² 4s²
V	23	[Ar] 3d³ 4s²
Cr	24	[Ar] 3d⁵ 4s¹
Mn	25	[Ar] 3d⁵ 4s²
Fe	26	[Ar] 3d⁶ 4s²
Co	27	[Ar] 3d⁷ 4s²
Ni	28	[Ar] 3d⁸ 4s²
Cu	29	[Ar] 3d¹⁰ 4s¹
Zn	30	[Ar] 3d¹⁰ 4s²
Ga	31	[Ar] 3d¹⁰ 4s² 4p¹
Ge	32	[Ar] 3d¹⁰ 4s² 4p²
As	33	[Ar] 3d¹⁰ 4s² 4p³
Se	34	[Ar] 3d¹⁰ 4s² 4p⁴
Br	35	[Ar] 3d¹⁰ 4s² 4p⁵
Kr	36	[Ar] 3d¹⁰ 4s² 4p¹

Table 15 Real Wavefunctions for One-electron Atomic Orbitals

n		Orbital
1	0	1s
2	0	2s
2	1	2p_z
2	1	2p_x
2	1	2p_y
3	0	3s
3	1	3p_z
3	1	3p_x
3	1	3p_y
3	2	3d_z2
3	2	3d_x2_-y2
3	2	3d_xy
3	2	3d_xz
3	2	3d_yz
4	0	4s
4	1	4p_z
4	1	4p_x
4	1	4p_y
4	2	4d_z2
4	2	4d_x2_-y2
4	2	4d_xy