Stirling’s approximation An ap-
proximation for the factorial, n!, of a
number n. The precise form of Stir-
ling’s approximation is:
n! = (2π)½nn+½exp(–n)This approximation is valid for large
values of n, being accurate for n
greater than about 10. A simpliÜed
version of Stirling’s expression is
logen! = nlogen – n, which is an ap-
proximation to the precise form, de-
rived by dropping all those terms
that do not increase at least as
quickly as n. An important applica-
tion of Stirling’s approximation is in
the derivation of the Boltzmann dis-
tribution (see boltzmann equation).
In this application n is very much
greater than 10, enabling the
simpliÜed version of Stirling’s ap-
proximation to be used.
STM See scanning tunnelling
microscope.
stochastic process Any process in
which there is a random element.
Stochastic processes are important in
nonequilibrium statistical mechan-
ics and disordered solids. In a time-
dependent stochastic process, a
variable that changes with time does
so in such a way that there is no cor-
relation between different time inter-
vals. An example of a stochastic
process is Brownian movement.
Equations, such as the Langevin
equation and the *Fokker–Planck
equation, that describe stochastic
processes are called stochastic equa-
tions. It is necessary to use statistical
methods and the theory of probabil-
ity to analyse stochastic processes
and their equations.
Stockholm Convention See per-
sistent organic pollutant.
stoichiometric Describing chemi-
cal reactions in which the reactants
combine in simple whole-number ra-
tios.
stoichiometric coefÜcientSee
chemical equation.stoichiometric compoundA
compound in which atoms are com-
bined in exact whole-number ratios.
Compare nonstoichiometric com-
pound.
stoichiometric mixture A mix-
ture of substances that can react to
give products with no excess reac-
tant.stoichiometric sumSee chemical
equation.stoichiometryThe relative propor-
tions in which elements form com-
pounds or in which substances react.
stokesSymbol St. A c.g.s. unit of
kinematic viscosity equal to the ratio
of the viscosity of aÛuid in poises to
its density in grams per cubic cen-
timetre. 1 stokes = 10–4m^2 s–1. It is
named after the British mathemati-
cian and physicist Sir George Gabriel
Stokes (1819–1903).
Stokes radiationThe electromag-
netic radiation that occurs in the
*Raman effect when the frequency
of the scattered radiation is lower
than the frequency of the unscat-
tered radiation, i.e. energy is trans-
ferred from the photon to the
scattering molecule. The spectral
Raman lines corresponding to this
type of radiation are called Stokes
lines, with the set of Stokes lines
being called the O-branchof the
Raman spectrum.
Similarly, *anti-Stokes radiation is
the radiation when the frequency of
the scattered electromagnetic radia-
tion is higher than the frequency of
the unscattered radiation, i.e. energy
is transferred to the photon from the
scattering molecule. The spectral
Raman lines corresponding to this
type of radiation are called anti-
Stokes lines, with the set of anti-505 Stokes radiation
s