found by *quantum mechanics of
free electrons in a uniform magnetic
Üeld. These energy levels, named
after the Soviet physicist Lev Davi-
dovich Landau (1908–68), who
analysed the problem in 1930, have
discrete values, which are integer
multiples of heB/m, where h is the
Planck constant, e is the charge of
the electron, m is the mass of the
electron, and B is the magneticÛux
density. Each Landau level is a highly
*degenerate level, with each level
beingÜlled by 2eB/h, where the factor
2 is due to the spin of the electron.
Landé interval ruleA rule used in
interpreting atomic spectra stating
that if the *spin–orbit coupling is
weak in a given multiplet, the energy
differences between two successive J
levels (where J is the total resultant
angular momentum of the coupled
electrons) are proportional to the
larger of the two values of J. The rule
was stated by the German-born US
physicist Alfred Landé (1888–1975) in- It can be deduced from the
quantum theory of angular momen-
tum. In addition to assuming Rus-
sell–Saunders coupling, the Landé
interval rule assumes that the inter-
actions between spin magnetic mo-
ments can be ignored, an assumption
that is not correct for very light
atoms, such as helium. Thus the
Landé interval rule is best obeyed by
atoms with medium atomic num-
bers.
Langevin equationA type of ran-
dom equation of motion (see sto-
chastic process) used to study
Brownian movement. The Langevin
equation can be written in the form
v
.
= ξv + A(t), where v is the velocity of
a particle of mass m immersed in a
Ûuid and v.
is the acceleration of the
particle; ξv is a frictional force result-
ing from the viscosity of theÛuid,
with ξbeing a constant frictioncoefÜcient, and A(t) is a random force
describing the average effect of the
Brownian motion. The Langevin
equation is named after the French
physicist Paul Langevin (1872–1946).
It is necessary to use statistical meth-
ods and the theory of probability to
solve the Langevin equation.Langmuir adsorption isotherm
An equation used to describe the
amount of gas adsorbed on a plane
surface, as a function of the pressure
of the gas in equilibrium with the
surface. The Langmuir adsorption
isotherm can be written:
θ= bp/(1 + bp),
where θis the fraction of the surface
covered by the adsorbate, p is the
pressure of the gas, and b is a con-
stant called the adsorption coefÜ-
cient, which is the equilibrium
constant for the process of adsorp-
tion. The Langmuir adsorption
isotherm was derived by the US
chemist Irving Langmuir (1881–
1957), using the *kinetic theory of
gases and making the assumptions
that:
(1) the adsorption consists entirely of
a monolayer at the surface;
(2) there is no interaction between
molecules on different sites and each
site can hold only one adsorbed mol-
ecule;
(3) the heat of adsorption does not
depend on the number of sites and is
equal for all sites.
The Langmuir adsorption isotherm is
of limited application since for real
surfaces the energy is not the same
for all sites and interactions between
adsorbed molecules cannot be ig-
nored.
Langmuir–BlodgettÜlmAÜlm
of molecules on a surface that can
contain multiple layers ofÜlm. A
Langmuir–BlodgettÜlm with multi-
ple layers can be made by dipping a
plate into a liquid so that it is cov-Landé interval rule 314l