Checklist Ch 07

7/30/2019 Checklist Ch 07

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Atkins & de Paula:

Atkins Physical Chemistry 9e

Checklist of key ideas

Chapter 7: Quantum Theory:

Introduction and Principles


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Chapter 7: Quantum Theory: Introduction and Principles

classical mechanics, the laws of motion introduced in the

seventeenth century by Isaac Newton.

quantum mechanics, the laws of motion introduced in thetwentieth century by Heisenberg and Schrdinger.

THE ORIGINS OF QUANTUM MECHANICS

electromagnetic field, an oscillating electric and magnetic

disturbance that spreads as a harmonic wave through space.

electric field, a field that acts on charged particles.

magnetic field, a field that acts on moving charged

particles.


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wavelength,, the peak-to-peak distance of a wave.

frequency,v, the number of times per second that a

displacement returns to its initial value.

wavenumber, v , the reciprocal of the wavelength.

electromagnetic spectrum, the range of frequencies

exhibited by the electromagnetic field and its classificationinto regions.

7.1 The failures of classical physics

black body, an object capable of emitting and absorbing al

frequencies of radiation uniformly.


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7.1 The failures of classical physics (cont)

RayleighJeans law, dE= d, = 8kT/4.

density of states,, the proportionality constant between thrange of wavelengths and the energy density in that range: d

= d.

ultraviolet catastrophe, the divergence of the energydensity of black-body radiation at high frequencies.

quantization of energy, the limitation of energies to discret

values.

Plancks constant, h = 6.626 08 1034 J s.


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Planck distribution, dE=d, = (8hc/5)/(ehc/kT 1).

Dulong and Petits law: the molar heat capacities of all

monatomic solids are the same, and close to 25 J K1

mol1

.

Einstein formula, CV,m = 3Rf,f= (E/T)2{e

_E/2T/(e

_E/T 1)}

Einstein temperature, E = hv/k.

Debye formula, CV,m = 3Rf, ( )

D

34

/

20D

e

3 de 1

xT

x

T x

f x

=

.

7.1 The failures of classical physics (cont..)


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Debye temperature,D = hvD/k.

spectrum, the record of intensity of light transmitted,absorbed, or scattered as a function of frequency,

wavelength, or wavenumber.

spectroscopy, the detection and analysis of a spectrum.

spectroscopic transition, a change of state that gives rise

to a feature in spectrum.

Bohr frequency transition, the relation between the

change in energy and the frequency of the radiation

emitted or absorbed: E= hv.

7.1 The failures of classical physics (cont..)


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7.2 Waveparticle duality

photon, a particle of electromagnetic radiation.

photoelectric effect,

the ejection of electrons from metals when they areexposed to ultraviolet radiation: mev2

= hv .

work function,, the energy required to remove an electron from the

metal to infinity .

DavissonGermer experiment, the diffraction of electrons by a crystal.

electron diffraction, the diffraction of electrons by an object in their path.

de Broglie relation, = h/p.

waveparticle duality, the joint particle and wave character of matter

and radiation.


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THE DYNAMICS OF MICROSCOPIC SYSTEMS

wavefunction,, a mathematical function obtained by solving

the Schrdinger equation and which contains all the dynamical

information about a system.

7.3 The Schrdinger equation

time-independent Schrdinger equation,(

2/2m)(d

2/dx

2) + V(x)= E.

7.4 The Born interpretation of the wavefunctionBorn interpretation, the value of ||

2at a point is proportional

to the probability of finding the particle at that point.


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7.4 The Born interpretation of the wavefunction (cont..)

Born interpretation, the value of ||2

at a point is proportional

to the probability of finding the particle at that point.

probability density, the probability of finding a particle in a

region divided by the volume of the region.

probability amplitude, the square-root of the probability

density (the wavefunction itself).

normalization constant, N= 1/{* dx}1/2.

spherical polar coordinates, the radius r, the colatitude , and

the azimuth . The volume element in spherical coordinates isr2sin drdd.

quantization, confinement of a dynamical observable to

discrete values.


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constraints on the wavefunction, the conditions a

wavefunction must obey (be continuous, have a continuous firs

derivative, be single-valued, and be square-integrable).

QUANTUM MECHANICAL PRINCIPLES

7.5 The information in a wavefunctionnode, a point where a wavefunction passes through zero .

operator, something that carries out a mathematical operation

on a function.

hamiltonian operator, the operator for the total energy of a

system, EH = .

7.4 The Born interpretation of the wavefunction (cont..)


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eigenvalue, the constant in the eigenvalue equation = .

eigenfunction, the function in the eigenvalue equation = .

eigenvalue equation, an equation of the form = .

observable, measurable properties of a system.

position operator, x = x.

momentum operator, px = (/i)d/dx.

hermitian operator, an operator for which it is true that

{ }

= dxdx ijji

7.5 The information in a wavefunction (cont..)


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orthogonal functions, i*j d = 0.

linear combination of two functions, c1f+ c2g.

superposition, a linear combination of wavefunctions.

complete set of functions, functions that can be used to

express any arbitrary function as a linear combination.

expectation value, d= .

7.6 The uncertainty principle

Heisenberg uncertainty principle: it is impossible to

specify simultaneously, with arbitrary precision, both the

momentum and the position of a particle; 21 qp .

7.5 The information in a wavefunction (cont..)


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wave packet, a localized wavefunction formed by

superimposing a series of wavefunctions.complementary observables, observables corresponding

to non-commuting operators.

commuting operators, operators for which 0, 21 = .

commutator,122121

, =

general form of the Heisenberg uncertainty principle:

[ ]2121 ,2

1

7.6 The uncertainty principle (cont..)


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Atomic Units

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al/mol627.5095kc27.21eV:energy14:typermittivivacuum

11029177.54

aradiusBohr:length

1)10(1.602176e:charge

11010938.9m:electronanofmass

12

h

unitatomicSI

3

00

11-

2

2

00

19-

31-

e

==

=

==

=

=

mem

C

kg

e

Checklist Ch 07

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