or absorbed radiation of frequency ν,
the electron jumped from one orbit
to another; the energy emitted or absorbed by each jump is equal to hν.
This theory gave good results in predicting the lines observed in the
spectrum of hydrogen and simple
ions such as He
+ , Li
2+ , etc. The idea of
quantized values of angular momentum was later explained by the wave
nature of the electron. Each orbit has
to have a whole number of wavelengths around it; i.e. nλ = 2πr, where
λ is the wavelength and n a whole
number. The wavelength of a particle
is given by h/mv, so nh/mv = 2πr,
which leads to mvr = nh/2π. Modern
atomic theory does not allow subatomic particles to be treated in the
same way as large objects, and Bohr’s
reasoning is somewhat discredited.
However, the idea of quantized angular momentum has been retained.
boiling point (b.p.) The temperature at which the saturated vapour
pressure of a liquid equals the external atmospheric pressure. As a consequence, bubbles form in the liquid
and the temperature remains constant until all the liquid has evaporated. As the boiling point of a liquid
depends on the external atmospheric
pressure, boiling points are usually
quoted for standard atmospheric
pressure (760 mmHg = 101 325 Pa).
boiling-point–composition diagram A graph showing how the
boiling point and vapour composition of a mixture of two liquids depends on the composition of the
mixture. The abscissa shows the
range of compositions from 100% A
at one end to 100% B at the other.
The diagram has two curves: the
lower one gives the boiling points (at
a Üxed pressure) for the different
compositions. The upper one is plotted by taking the composition of
vapour at each temperature on the
boiling-point curve. The two curves
would coincide for an ideal mixture,
but generally they are different because of deviations from *Raoult’s
law. In some cases, they may show a
maximum or minimum and coincide
at some intermediate composition,
explaining the formation of
*azeotropes.
boiling-point elevation See
elevation of boiling point.
Boltzmann, Ludwig Eduard
(1844–1906) Austrian physicist. He
held professorships in Graz, Vienna,
Munich, and Leipzig, where he
worked on the kinetic theory of
gases (see maxwell–boltzmann distribution) and on thermodynamics
(see boltzmann equation). He suffered from depression and committed suicide.
Boltzmann constant Symbol k.
The ratio of the universal gas constant (R) to the Avogadro constant
(N A ). It may be thought of therefore
as the gas constant per molecule:
k = R/N A = 1.380 658(12) × 10
–23 J K
–1
It is named after Ludwig *Boltzmann.
Boltzmann equation An equation
used in the study of a collection of
particles in *nonequilibrium statistical mechanics, particularly their
transport properties. The Boltzmann
equation describes a quantity called
the distribution function, f, which
gives a mathematical description of
the state and how it is changing. The
distribution function depends on a
position vector r, a velocity vector v,
and the time t; it thus provides a statistical statement about the positions
and velocities of the particles at any
time. In the case of one species of
particle being present, Boltzmann’s
equation can be written
∂f/∂t + a.(∂f/∂v) + v.(∂f/∂r) = (∂f/∂t) coll ,
where a is the acceleration of bodies
boiling point
76
b
www.AzShimi.ir www.AzShimi.com
the electron jumped from one orbit
to another; the energy emitted or absorbed by each jump is equal to hν.
This theory gave good results in predicting the lines observed in the
spectrum of hydrogen and simple
ions such as He
+ , Li
2+ , etc. The idea of
quantized values of angular momentum was later explained by the wave
nature of the electron. Each orbit has
to have a whole number of wavelengths around it; i.e. nλ = 2πr, where
λ is the wavelength and n a whole
number. The wavelength of a particle
is given by h/mv, so nh/mv = 2πr,
which leads to mvr = nh/2π. Modern
atomic theory does not allow subatomic particles to be treated in the
same way as large objects, and Bohr’s
reasoning is somewhat discredited.
However, the idea of quantized angular momentum has been retained.
boiling point (b.p.) The temperature at which the saturated vapour
pressure of a liquid equals the external atmospheric pressure. As a consequence, bubbles form in the liquid
and the temperature remains constant until all the liquid has evaporated. As the boiling point of a liquid
depends on the external atmospheric
pressure, boiling points are usually
quoted for standard atmospheric
pressure (760 mmHg = 101 325 Pa).
boiling-point–composition diagram A graph showing how the
boiling point and vapour composition of a mixture of two liquids depends on the composition of the
mixture. The abscissa shows the
range of compositions from 100% A
at one end to 100% B at the other.
The diagram has two curves: the
lower one gives the boiling points (at
a Üxed pressure) for the different
compositions. The upper one is plotted by taking the composition of
vapour at each temperature on the
boiling-point curve. The two curves
would coincide for an ideal mixture,
but generally they are different because of deviations from *Raoult’s
law. In some cases, they may show a
maximum or minimum and coincide
at some intermediate composition,
explaining the formation of
*azeotropes.
boiling-point elevation See
elevation of boiling point.
Boltzmann, Ludwig Eduard
(1844–1906) Austrian physicist. He
held professorships in Graz, Vienna,
Munich, and Leipzig, where he
worked on the kinetic theory of
gases (see maxwell–boltzmann distribution) and on thermodynamics
(see boltzmann equation). He suffered from depression and committed suicide.
Boltzmann constant Symbol k.
The ratio of the universal gas constant (R) to the Avogadro constant
(N A ). It may be thought of therefore
as the gas constant per molecule:
k = R/N A = 1.380 658(12) × 10
–23 J K
–1
It is named after Ludwig *Boltzmann.
Boltzmann equation An equation
used in the study of a collection of
particles in *nonequilibrium statistical mechanics, particularly their
transport properties. The Boltzmann
equation describes a quantity called
the distribution function, f, which
gives a mathematical description of
the state and how it is changing. The
distribution function depends on a
position vector r, a velocity vector v,
and the time t; it thus provides a statistical statement about the positions
and velocities of the particles at any
time. In the case of one species of
particle being present, Boltzmann’s
equation can be written
∂f/∂t + a.(∂f/∂v) + v.(∂f/∂r) = (∂f/∂t) coll ,
where a is the acceleration of bodies
boiling point
76
b
www.AzShimi.ir www.AzShimi.com