Physical constants, useful mathematical relations. icon

Physical constants, useful mathematical relations.


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A PHYSICAL CONSTANTS 538

B USEFUL MATHEMATICAL RELATIONS 541

C ALPHABETICAL LIST OF THE ELEMENTS 544

D ATOMIC AND NUCLEAR DATA 546


A P P E N D I X

A

Physical Constants


NAMED CONSTANTS


Most constants are given first with three significant figures, since this is almost always sufficiently accurate. The last two columns give the mantissa of the best known value and its uncertainty in parts per million. For example, in the first entry, the best known value of the atomic mass unit is


1 u = 1.660540  10 27 kg


with an uncertainty of 0.6 part per million (so that the final zero is uncertain by about 1). All values were taken from E. R. Cohen and B. N. Taylor, Reviews of Modern Physics, vol. 59, p. 1139 (1987).




Name

Symbol and value

Best

mantissa

Uncertainty

(ppm)

Atomic mass unit

1 U = -L m(12C atom)

12

exact







= 1.66 10-27 kg

1660540

0.6




= 931.5 MeV/c2

9314943

0.3

Avogadro's constant

NA = 6.02  1023 particles/mol

6022137

0.6

Bohr magneton

yB = ehl(2rne)










= 5.79  10-5 eV/T

57883826

0.09




= 9.27  10-24 J/T (or A M2)

9274015

0.3

Bohr radius

aB = h 2 1(ke 2Me)










= 5.29  10-11 m

52917725

0.04

Boltzmann's constant

kB = 8.62  10-5 eV/K

861738

8




= 1.38  10-23 J/K

138066

8

Coulomb force constant

k = 1/(4 7rEo) = yo c '/(4 7r)

exact







= 8.99  109 N- M2/ c2

898755178 . . .




Electron Compton

A, = hl(MeC)







wavelength

= 2.43  10-11 m

24263106

0.09

Electron volt

1 eV = 1.60  10-19 J

16021773

0.3




Name

Symbol and value

Best

mantissa

Uncertainty

(ppm)

Elementary charge

e = 1.60  10-19 C

16021773

0.3

Fine-structure constant

a = ke 2/(h c)










= 7.30  10-3 ~ 1/137

72973531

0.04

Gas constant

R = 8.31 J/(mol - K)

831451

8




= 0.0821 liter - atm/(mol - K)

820578

8

Gravitational constant

G = 6.67  10-11 N- M2/kg2

66726

130

Mass of electron

Me = 5.49  10-4 U

54857990

0.02




= 9. 11  10-31 kg

9109390

0.6




= 0.511 MeV/ c2

5109991

0.3

Mass of proton

Mp = 1.007 u

100727647

0.01




= 1.673  10-27 kg

1672623

0.6




= 938.3 MeV/ c2

9382723

0.3

Mass of neutron

m. = 1.009 u

100866490

0.01




= 1.675  10-27 kg

1674929

0.6




= 939.6 MeV/ c2

9395656

0.3

Nuclear magneton

IUN = eh /(2 m,)










= 3.15  10-8 eV/T

31524517

0.09




= 5.05  10-27 J/T

5050787

0.3

Permeability of space

#0 = 47t  10-7 N/A2

exact







= 1.26  10-6 N/A2

125663706 . . .




Permittivity of space

E0 = ll(pOC2)

exact







= 8.85  10-12 c2/(N-M2)

885418781 . . .




Planck's constants

h = 6.63  10-34 J. s

6626076

0.6




= 4.14  10-11 eV-s

4135669

0.3




h= hl(27r)










= 1.05  10-34 J_s

10545727

0.6




= 6.58  10-16 eV - s

6582122

0.3

Rydberg constant

R = m,k2e4l(47reh 3)










= 1.10  10-2 nm-'

1097373153

0.001

Rydberg energy

ER = hcR = m,k2e4/(2 h 2)










= 13.6 eV

13605698

0.3

Speed of light

c = 3.00  108 m/s

299792458

exact




^ USEFUL COMBINATIONS




Best

mantissa

Uncertainty

(ppm)

hc = 1240 eV - nm = 1240 MeV - fm

12398424

0.3

h c = 197 eV - nm 197 MeV - fm

19732705

0.3

kel = 1.44 eV - nm 1.44 MeV - fm

14399652

0.3

NA  (1 u) = 1 gram

exact




kB T = 0.026 eV at room temperature (300 K)










^ CONVERSION FACTORS

Area:
















1 barn = 10-28 M2

exact







Energy:
















1 cal = 4.184 J

exact










1 eV = 1.60  10-19 J

16021773

0.3




Length:
















1 = 1 angstrom













= 10-10 m

exact










1 ft = 30.48 cm

exact










1 in = 2.54 cm

exact










1 mi = 1609 m

1609344

exact




Mass:
















1 lb(mass) = 0.454 kg

45359237

exact







1 MeV/c2 = 1.07  10-3 u

10735438

0.3







= 1.78  10-30 kg

17826627

0.3







1 u = -L m(12C atom)

exact










= 931.5 MeV/ c2

9314943

0.3







= 1.66  10-27 kg

1660540

0.6




Momentum:










1 MeV/c = 5.34  10-22 kg. m/s

5344288

0.3







^ SI PREFIXES

T

tera

1012

G

giga

109

M

mega

106

k

kilo

103




c

centi

10-2

m

milli

10-3

,u

micro

10-6

n

nano

10-9

P

Pico

10-12

f

femto

10-11

a

atto

10-18




A P P E N D I X

B

Useful Mathematical

Relations


TRIGONOMETRIC IDENTITIES


LAW OF COSINES


where A, B, C are the three sides of a triangle and 0 is the angle opposite C.





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