Stirling’s approximation An approximation for the factorial, n!, of a
number n. The precise form of Stirling’s approximation is:
n! = (2π)
½ n
n + ½ exp(–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
log e n! = nlog e n – n, which is an approximation to the precise form, derived by dropping all those terms
that do not increase at least as
quickly as n. An important application of Stirling’s approximation is in
the derivation of the Boltzmann distribution (see boltzmann equation).
In this application n is very much
greater than 10, enabling the
simpliÜed version of Stirling’s approximation 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 mechanics and *disordered solids. In a timedependent stochastic process, a
variable that changes with time does
so in such a way that there is no correlation between different time intervals. 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 equations. It is necessary to use statistical
methods and the theory of probability to analyse stochastic processes
and their equations.
Stockholm Convention See persistent organic pollutant.
stoichiometric Describing chemical reactions in which the reactants
combine in simple whole-number ratios.
stoichiometric coefÜcient See
chemical equation.
stoichiometric compound A
compound in which atoms are combined in exact whole-number ratios.
Compare nonstoichiometric compound.
stoichiometric mixture A mixture of substances that can react to
give products with no excess reactant.
stoichiometric sum See chemical
equation.
stoichiometry The relative proportions in which elements form compounds or in which substances react.
stokes Symbol St. A c.g.s. unit of
kinematic viscosity equal to the ratio
of the viscosity of a Ûuid in poises to
its density in grams per cubic centimetre. 1 stokes = 10
–4 m
2 s
–1
. It is
named after the British mathematician and physicist Sir George Gabriel
Stokes (1819–1903).
Stokes radiation The electromagnetic radiation that occurs in the
*Raman effect when the frequency
of the scattered radiation is lower
than the frequency of the unscattered radiation, i.e. energy is transferred 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-branch of the
Raman spectrum.
Similarly, *anti-Stokes radiation is
the radiation when the frequency of
the scattered electromagnetic radiation 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 antiStokes lines, with the set of anti505
Stokes radiation
s
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number n. The precise form of Stirling’s approximation is:
n! = (2π)
½ n
n + ½ exp(–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
log e n! = nlog e n – n, which is an approximation to the precise form, derived by dropping all those terms
that do not increase at least as
quickly as n. An important application of Stirling’s approximation is in
the derivation of the Boltzmann distribution (see boltzmann equation).
In this application n is very much
greater than 10, enabling the
simpliÜed version of Stirling’s approximation 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 mechanics and *disordered solids. In a timedependent stochastic process, a
variable that changes with time does
so in such a way that there is no correlation between different time intervals. 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 equations. It is necessary to use statistical
methods and the theory of probability to analyse stochastic processes
and their equations.
Stockholm Convention See persistent organic pollutant.
stoichiometric Describing chemical reactions in which the reactants
combine in simple whole-number ratios.
stoichiometric coefÜcient See
chemical equation.
stoichiometric compound A
compound in which atoms are combined in exact whole-number ratios.
Compare nonstoichiometric compound.
stoichiometric mixture A mixture of substances that can react to
give products with no excess reactant.
stoichiometric sum See chemical
equation.
stoichiometry The relative proportions in which elements form compounds or in which substances react.
stokes Symbol St. A c.g.s. unit of
kinematic viscosity equal to the ratio
of the viscosity of a Ûuid in poises to
its density in grams per cubic centimetre. 1 stokes = 10
–4 m
2 s
–1
. It is
named after the British mathematician and physicist Sir George Gabriel
Stokes (1819–1903).
Stokes radiation The electromagnetic radiation that occurs in the
*Raman effect when the frequency
of the scattered radiation is lower
than the frequency of the unscattered radiation, i.e. energy is transferred 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-branch of the
Raman spectrum.
Similarly, *anti-Stokes radiation is
the radiation when the frequency of
the scattered electromagnetic radiation 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 antiStokes lines, with the set of anti505
Stokes radiation
s
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