found by *quantum mechanics of
free electrons in a uniform magnetic
Üeld. These energy levels, named
after the Soviet physicist Lev Davidovich 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 magnetic Ûux
density. Each Landau level is a highly
*degenerate level, with each level
being Ülled by 2eB/h, where the factor
2 is due to the spin of the electron.
Landé interval rule A 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
1923. It can be deduced from the
quantum theory of angular momentum. In addition to assuming *Russell–Saunders coupling, the Landé
interval rule assumes that the interactions between spin magnetic moments 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 numbers.
Langevin equation A type of random equation of motion (see stochastic 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 resulting from the viscosity of the Ûuid,
with ξ being a constant friction
coefÜcient, 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 methods 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 θ is the fraction of the surface
covered by the adsorbate, p is the
pressure of the gas, and b is a constant called the adsorption coefÜcient, which is the equilibrium
constant for the process of adsorption. 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 molecule;
(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 ignored.
Langmuir–Blodgett Ülm A Ülm
of molecules on a surface that can
contain multiple layers of Ülm. A
Langmuir–Blodgett Ülm with multiple layers can be made by dipping a
plate into a liquid so that it is covLandé interval rule
314
l
www.AzShimi.ir www.AzShimi.com
free electrons in a uniform magnetic
Üeld. These energy levels, named
after the Soviet physicist Lev Davidovich 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 magnetic Ûux
density. Each Landau level is a highly
*degenerate level, with each level
being Ülled by 2eB/h, where the factor
2 is due to the spin of the electron.
Landé interval rule A 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
1923. It can be deduced from the
quantum theory of angular momentum. In addition to assuming *Russell–Saunders coupling, the Landé
interval rule assumes that the interactions between spin magnetic moments 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 numbers.
Langevin equation A type of random equation of motion (see stochastic 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 resulting from the viscosity of the Ûuid,
with ξ being a constant friction
coefÜcient, 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 methods 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 θ is the fraction of the surface
covered by the adsorbate, p is the
pressure of the gas, and b is a constant called the adsorption coefÜcient, which is the equilibrium
constant for the process of adsorption. 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 molecule;
(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 ignored.
Langmuir–Blodgett Ülm A Ülm
of molecules on a surface that can
contain multiple layers of Ülm. A
Langmuir–Blodgett Ülm with multiple layers can be made by dipping a
plate into a liquid so that it is covLandé interval rule
314
l
www.AzShimi.ir www.AzShimi.com