Reference tables

APPENDIX

IX

REFERENCE TABLES

PHYSICAL AND MATHEMATICAL CONSTANTS Value Quantity

Symbol

SI

CGS emu

Permeability of the vacuum

µ0

4π × 10–7 kg m s–2 A–2

1

Speed of light in the vacuum

c

2.9979 × 108 m s–1

2.9979 × 1010 cm s–1

Elementary charge (absolute value of the electron charge)

e

1.6022 × 10–19 A s

1.6022 × 10–20 abcoulombs

Planck constant

h

6.6261 × 10–34 J s

6.6261 × 10–27 erg s

ħ = h/2π

1.0546 × 10–34 J s rad–1

1.0546 × 10–27 erg s rad–1

NA

6.0221 × 1023 mol–1

6.0221 × 1023 mol–1

Physical constants

Avogadro constant

–30

Electron rest mass

me

0.9109 × 10

kg

0.9109 × 10–27 g

Proton rest mass

mp

1.6726 × 10–27 kg

1.6726 × 10–24 g

Free-spin electron g factora

ge

2.0023

Electron Bohr magneton

2.0023

µB

9.2740 × 10

–1

9.2740 × 10–21 erg G–1

Nuclear Bohr magneton

µN

5.0508 × 10–27 J T–1

5.0508 × 10–24 erg G–1

Free-electron magnetic moment

µe = −

–9.2848 × 10–24 J T–1

–9.2848 × 10–21 erg G–1

Proton magnetic moment

µp =

1.4106 × 10–26 J T–1

1.4106 × 10–23 erg G–1

Electron-to-proton magnetic moments ratio

|µe/µp|

658.21

658.21

Free-electron magnetogyric ratioa

γe

–1.7609 × 1011 rad s–1 T–1

Proton magnetogyric ratio

γp

2.6752 × 10 rad s T

Boltzmann constant

k

1.3807 × 10–23 J K–1

Hyperfine coupling constant of the hydrogen atom

–24

ge µ B 2 g pµN

JT

2

(A/(h))H (A/(ħ))H

8

9

–1

1.4204 × 10 Hz 8.9247 × 109 rad s–1

–1

–1.7609 × 107 rad s–1 G–1 2.6752 × 104 rad s–1 G–1 1.3807 × 10–16 erg K–1 1.4204 × 109 Hz 8.9247 × 109 rad s–1 (Continued)

NMR of Paramagnetic Molecules. http://dx.doi.org/10.1016/B978-0-444-63436-8.00021-1 Copyright © 2017 Elsevier B.V. All rights reserved.

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APPENDIX IX Reference tables

Quantity

Symbol

Value

e

2.7183

π

3.1416

Mathematical constants

The electron spin possesses a negative γ and therefore a negative ge. However, it is common practice to use a positive ge and to revert the sign of all equations involving ge [Eq. (1.10)]. a

CONVERSION FACTORS To Convert From

To

Multiply by

Length

Ångström (Å)

meter (m)

1 × 10–10

Pressure

atmosphere (atm)

Pascal (Pa) (kg m–1 s–2)

1.01325 × 105

Mass

atomic mass unit (amu)

kilogram (kg)

1.6606 × 10–27

Energy

calories (cal)

Joule (J)

4.1840

electron volt (eV)

Joule (J)

1.6022 × 10–19

kilowatt-hour (kWh)

Joule (J)

3.6 × 106

–1

–1

Viscosity

centipoise

kg m s

Angles

degree (deg)

radian (rad)

Volume Frequency

1 × 10–3 0.017453 3

liter (1) –1

radian/second (rad s ) –1

wavenumber (cm )

cubic meter (m )

1 × 10–3

cycle/second (cps) (Hz)

0.15915

energy (J)

1.9865 × 10–23

frequency (s–1) (Hz)

2.9979 × 1010

–1

Temperature

frequency (rad s )

1.8837 × 1011

cycle/second (cps) (Hz)

energy (J)

6.6262 × 10–34

Kelvin (K)

energy (J)

1.3807 × 10–23 –1

wavenumber (cm )

0.69467

SOME PHYSICAL QUANTITIES AND THEIR SI UNITS Electric charge (quantity of electricity)

Q

C

As

Electric current

i

A

A

Electric potential

V

V

kg m2 s–3 A–1 (= J A–1 s–1)

Energy

E

J

kg m2 s–2

APPENDIX IX Reference tables

Frequency

ν

Hz

s–1

Frequency (angular velocity)

w

rad s–1

rad s–1

Magnetic field strength

H

A m–1

A m–1

Magnetic induction (flux density)

B

T

kg A–1 s–2

Magnetic moment

µ

J T–1

A m2

Magnetic susceptibility

χ

m3

m3 –1

–3

Magnetization

M

JT m

A m–1

Magnetogyric ratio

Γ

rad s–1 T–1

rad A s kg–1

Molar magnetic susceptibility

χM

m3 mol–1

m3 mol–1

Power

P

W

kg m2 s–3 (=J s–1)

Viscosity (dynamic)

η

kg m–1 s–1

kg m–1 s–1

487