LagrangianSymbol L. A function
used to deÜne a dynamical system in
terms of functions of coordinates, ve-
locities, and times given by:
L = T – Vwhere T is the kinetic energy of the
system and V is the potential energy
of the system. The Lagrangian formu-
lation of dynamics has the advantage
that it does not deal with many vec-
tor quantities, such as forces and ac-
celerations, but only with two scalar
functions, T and V. This leads to great
simpliÜcations. Lagrangian dynamics
was formulated by Joseph Louis La-
grange (1736–1813).
LAH Lithium aluminium hydride;
see lithium tetrahydro-
aluminate(iii).
lake A pigment made by combining
an organic dyestuff with an inorganic
compound (usually an oxide, hydrox-
ide, or salt). Absorption of the or-
ganic compound on the inorganic
substrate yields a coloured complex,
as in the combination of a dyestuff
with a *mordant. Lakes are used in
paints and printing inks.
lambda point See superfluidity.
Lamb-dip spectroscopy A spec-
troscopic technique enabling the cen-
tres of absorption lines to be
determined very precisely by making
use of the Doppler shift associated
with very rapidly moving molecules.
An intense monochromatic beam of
radiofrequency electromagnetic radi-
ation is passed through a sample of a
gas with the frequency being slightly
higher than that of maximum ab-
sorption. Only certain molecules
moving at a certain speciÜc speed
can absorb radiation. The beam is
then reÛected back through the sam-
ple so that radiation is absorbed by
molecules moving at exactly this
same speed, except that they are
moving away from the mirror. If the
radiation is exactly at the absorption
peak, only molecules moving perpen-
dicular to the line of the beam
(which hence have no Doppler shift)
absorb both in the initial path and
the reÛected path of the radiation.
Since molecules being excited in the
initial path leave fewer molecules to
be excited in the return path this
causes a less intense absorption to be
observed. As a result a dip appears in
the curve, thus enabling the absorp-
tion peak to be found very accu-
rately. Lamb-dip spectroscopy is
named after Willis Eugene Lamb
(1913–2008).Lamb shiftA small energy differ-
ence between two levels (^2 S1/2and(^2) P1/2) in the hydrogen spectrum. The
shift results from the quantum inter-
action between the atomic electron
and the electromagnetic radiation. It
wasÜrst explained by Willis Eugene
Lamb.
lamellar solidsSolid substances in
which the crystal structure has dis-
tinct layers (i.e. has a layer lattice).
The micas are an example of this
type of compound. *Intercalation
compounds are lamellar compounds
formed by interposition of atoms,
ions, etc., between the layers of an
existing element or compound. For
example, graphite is a lamellar solid.
With strong oxidizing agents (e.g. a
mixture of concentrated sulphuric
and nitric acids) it forms a nonstoi-
chiometric ‘graphitic oxide’, which is
an intercalation compound having
oxygen atoms between the layers of
carbon atoms. Substances of this type
are called graphitic compounds.
lamp blackAÜnely divided (micro-
crystalline) form of carbon made by
burning organic compounds in
insufÜcient oxygen. It is used as a
black pigment andÜller.
Landau levelsThe energy levels
313 Landau levels
l