The following reference information should appear on page i of the preliminary pages

General data and fundamental constants

~

Quantity Value Powerof ten Units_______ __~ __ ~_...JSymbol

Speed oflight c 2.997925 58*

Elementary charge e 1.602 176

Faraday constant 9.64853

Boltzmann constant k 1.38065

Gas constant 8.31447

8.31447

8.20574

6.23637

Planck's constant h

n =h/2n

Avogadro's constant

Atomic mass unit u 1.66054

10-19 C

C'mol!

10-23

10-2

10-2

10

JK-I mol'

L bar K-I mol!

L atm K-1mol"!

L TorrK-1 mol-I

10-34

10-34Js

Js

1023 mol!

10-27 kg

Mass

electron me 9.10938 10-31 kg

proton mp1.672 62 10-27 kg

neutron mn

1.67493 10-27 kg

Vacuum permittivity

1.11265

8.85419 10-12

10-10

Vacuum permeability flo 4n 10-7 J S2C-2 m-I (= T2 J-I m").................................................................................................................................................................................................................................................

Magneton

Bohr flB = en/2me

9.27401

nuclear flN = enj2mp

5.05078

g value ge 2.002 32...... , , .

Bohr radius Go = 4neon2/mee2 5.291 77 10-11 m

.................................................................................................................................................................................................................................................

Fine-structure constant a = floe2c/2h 7.29735 10-3

a-I 1.37036 102

10-24

10-27

Second radiation constant c2= hc/k 1.43878 10-2 m K••••••••••••••. « •••••••••• ' •••••••••••••••••••••••••••••••• , •••••••••••••••••••••••••••••••••• ,., .•••••• , •.•••• " ••••••••••••••••••••• , •.•••• , ••••••••••••••• , ••••••• , •••••••••••••••••••••••••••••••••••••••••• , •••••••••••••••••• , •••• " •••••••

Stefan-Boltzmannconstant u=2n5k4/15h3c2 5.67051 10-8 Wm-2K-4..................... ,., " ,.., ,' , ,' - ,' " .

Rydberg constant R = mee4/8h3cc~ 1.09737 105 crrr '

Standard acceleration offree fall g 9.80665* m S-2., , .

Gravitational constant G 6.673 10-11 N m? kg-2

*Exact value

The Greek alphabet

A,a alpha H,1J eta N,v nu Y,v upsilon

B,fJ beta e,e theta 3, ,; XI et>, IjJ phi

r,y gamma I, I iota n.» pi X,X chi

~,J delta K,K kappa P,p rho 'It, lfI psi

E,e epsilon A,}, lambda L,a sigma Q,w omega

Z,( zeta M,f.l mu T,7: tau

Mathematical relations

11:

e

3.141592 65359 .

2.71828182846 .

Integrals

Jx"dx = X"-

I

+ constantn+l

J± dx = In x + constant

{ex>x"e-axdx = ~Jo a"+!

Logarithms and exponentials

1nx + 1ny + ... = 1nxy ...

1nx - 1ny = In (xfY)

a 1nx = ln x"

Inx = (In 10) log x = (2.302585 ... ) logx

J sin? ax dx = t x - (ta) sin Zax + constant

Jsinaxsinbxdx = sin(a-b)x sin(a+b)x + constant2(a-b) 2(a +b)

if a2 *- b2

erf z = 2y, {o e-y2dyIt 2 Jz

(eX)a = eax

e± ix = cos x ± i sin x

Useful relations

Taylor expansions

At T = 298.15 K

RT 2.4790 kJ mol-I

RT/F 25.693 mV

RTln 10fF 59.160 mV

kT/he 207.226 crrr '

kT/e 25.693 meV

VBm 2.4790 x 10-2 m ' mol! = 24.790 L mol-1

f(x) = ~ -.L [dllf] (x-a)"~ nt dx"1l=0 a

ex = 1 + x + t x2 + ...

In x = (x - 1) - t (x - 1)2 + t (X - I? - t (x - 1)4 +

I (1 ) - I 2 I 3n +X -X-ZX +3X ...

_1_ = 1 - x + X2 ...

I+x

Conversion factors

[oy] [ox] [oz] - -1ox z OZ y oy x -

1.60218 x 10-19 J

96.485 kJ mol!

8065.5 cm :'

4.184* J

101.325* kPa

760* TOff

1 crrr ' 1.9864 x 10-23 J

1 D 3.33564 x 1O-30C m

1A lO-lom*

IT 104G*

1 L atm = 101.325 J*

e;oc = TfK-273.15*

1 cal

1 atm

1eV

Derivatives

d(f + g) = df + dg

d(fg) = fdg + gdf

I I Idd- = -df- - g

g g g2

df = dfdg

dt dg dt

(* Exact values)

dx" = nxr:'dx

JL eax = aeaxdx

Unit relations

Energy 1 J 1 kg m2 S-2

1AVs

Force IN 1 kg m S-2

Pressure 1 Pa = 1 Nm-2 = 1 kg m! s-2

1 J m -'

Charge 1C 1As

Potential difference IV 1 J C-I = 1 kg m? S-3A:'

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