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Atomic Models and the Old Quantum Theory
Giancarlo Borgonovi and Bill Scott
Presentation to the Lyncean Group
January 21, 2009
Selected milestones in the development of modern physics
Uhlenbeck
and
Goudsmit
Planck
Rutherford
Balmer
Bohr
Einstein
Sommerfeld
1900
1911
1886
1905
1900
1925
1913
1916
1923
Discovery Period
1928
Breakthrough
1964
Accomodation,
Development,
and application
Present
Baroque
Period
(Periodization according to J. Evans, Introduction to "Quantum Mechanics at the Crossroads",
Springer, Berlin 2007.)
Optical spectra
Hydrogen
Nitrogen
Joseph vonFraunhofer
1787 - 1826
Iodine
Balmer’s Contribution
1

 R(
1
1

)
2
2
2
n
n  3,4,5...
R  1.097 10 5 cm 1
Johann Balmer
1825 - 1898
Spectral Series
Regularity
S P D F
Terms
Walter Ritz
1878 - 1909
Johannes Rydberg
1854 - 1919
Max Planck and the introduction of the quantum
• In 1900 Max Planck explained the
Max Planck
1858 - 1947
distribution of frequencies in the spectrum of
blackbody radiation by assuming that energy
exchanges are discrete rather then continuous.
• The Planck constant h = 6.55 x 10-27 erg sec
can be considered the building block of
quantum mechanics.
• h is a unit of action (energy x time) as well as
angular momentum.
• Angular momentum in quantum physics can
only appear in discrete amounts, multiples of
h/2π or of 1/2(h/2π).
u  A 3e  b / T
2
u  kT 2 3
 c
8 3
h
u  3 h / kT
c e
1
Planck assumed the radiation was at
equilibrium with vibrating charges in
the walls of the black box.
E  nh
Einstein and the photoelectric effect
In 1905 Einstein explained the photoelectric effect (observed
by Hertz in 1988, studied systematically by Lenard in 1902)
as follows:
• By adopting the quantum hypothesis introduced by Max
Planck.
• Assuming that the energy in a lightwave is not distributed
uniformly, but in quanta which later became known as
photons.
Albert Einstein
1879 - 1955
• Emission of an electron takes place only afterthe electron
has absorbed all the energy of the photon.
Evolution of atom models
J.J Thomson
1898
1908
Louis de Broglie
1923
Rutherford and Bohr
1911
1913
Schrödinger
1926
Rutherford and the nucleus
• From New Zealand toEngland, then to Canada, back to England
• Discovered both alpha and beta rays
• Nobel prize for chemistry
• Backscattering of alpha particles (Geiger-Marsden experiment)
• Emission of protons from nitrogen by bombardment with alpha
particles
Ernest Rutherford
1871 - 1937
• First disintegration of nuclei using accelerators (Cockroft and
Walton)
$100 New Zealand Banknote
Hans Geiger
1882 - 1945
Ernest Marsden
1889 - 1970
Description of Rutherford experiment
The few high angle scatterings showed the
nucleus must be very small.
Niels Bohr
• Worked at Manchester with Rutherford
• Developed first quantum model of the atom, for
Hydrogen and ionized helium
• Model predicted Balmer formula, including
quantitative calculation of Rydberg constant
• Explanation of periodic table
• Principle of correspondence
• Principle of complementarity
Niels Bohr
1885 - 1962
• Was the force behind the Copenhagen institute of
theoretical physics
• Was one of the major figures in physics in the past
century
• Was deeply involved in world issues
Description of Bohr atom
• The force field between nucleus and electron is Coulombian, with central field. As
a result the motion of the electron is such that the angular momentum remains
constant.
• Electrostatic attraction nucleus - electron balances the centrifugal force.
• Assumption 1: only those orbits for which angular momentum is a multiple of h/2π
are allowed (stationary states of constant energy).
• Assumption 2: emission (absorption) of light takes place when the electron
transitions from one state to another, following the Planck relationship E2-E1=hν
mv 2 e 2 Z
 2
r
r
mvr  n
h
2π
(n  1,2,3....)
Sommerfeld elliptic orbits
Arnold Sommerfeld
1868 - 1951
• Introduced elliptic orbits to explain
spectra of atoms other then hydrogen or
ionized helium.
• Introduced magnetic quantum number
• Introduced inner quantum number
The limits of the old quantum theory
The old quantum theory was reasonably successful in explaining the spectra
of atoms with one electron in the last shell.
owever, it failed miserably in trying to explain the spectrum of helium.
The spectra of atoms such as helium (and also fine structure, Zeeman effect)
were fully understood only after the appearance of quantum mechanics.
2S
•
1/2
3P
0
2D
3/2
3F
2
The introduction of semi-integer quantum numbers
(1921) came before the introduction of spin (1925)
Alfred Landé
1888 - 1976
De Broglie matter wave - explanation of quantization
Louis de Broglie
1892 - 1987
To every particle can be associated a wave whose wavelength is inversely
proportional to its momentum ( λ =h/p )
•
• Was confirmed by electron diffraction in 1927 (Davisson and Germer)
The living Bohr atom - current research
Physicists create millimeter-sized 'Bohr atom'
Generation of quasiclassical Bohr -like wave packets using half-cycle pulses
J. J. Mestayer, B. Wyker, F. B. Dunning, C. O. Reinhold, S. Yoshida, and J. Burgdörfer
We demonstrate the experimental realization of Bohr -like atoms by applying a pulsed
unidirectional field, termed a half-cycle pulse (HCP), to atoms in quasi-two-dimensional nearcircular states. This leads to creation of localized wave packets that travel in near-circular orbits
and mimic the dynamics of an electron in the original Bohr model of the hydrogen atom. This
motion can be followed for several orbital periods before the localization of the wave packet is
lost due to dephasing. We show, however, that localization can be recovered by application of
further HCPs.
Phys. Rev. A 78, 045401 (2008)
Similarities between the old quantum theory and particle physics
• The elementary particles can be seen as
forming a spectrum in mass or energy.
Ξ
Σ
• Regularities are found to be associated with
this ‘spectrum’.
Δ
• Instead of multple levels due to spin there are
isospin multiplets.
p, n
ρ
η
π
ω
• In attempting to explain this ‘spectrum’
quantum numbers have been introduced, for
example strangeness, baryon number, isospin,
hypercharge.
• The color property of quarks and gluons seem
to have been introduced to save the Pauli
principle.
Conclusions
• The period of development of the old quantum theory (roughly 1900-1923) was a
heroic period, characterized by trials and errors.
• The discovery of the nucleus and the introduction of quantized orbits - a major
milestone in the middle of the period - worthy of being celebrated.
• Both Rutherford and Bohr were fascinating and charismatic personalities, who
left a legacy and inspired scores of researchers (Cavendish laboratory, Copenhagen
Institute).
• Methods and ideas developed within the framework of the old quantum theory,
although drastically changed by the appearance of QM, still maintained a practical
value in succeeding years (e.g. notations for electronic states, and interpretation of
optical spectra).