Atomic Models and the Old Quantum Theory

Giancarlo Borgonovi and Bill Scott

Presentation to the Lyncean Group

January 21, 2009

Discovery Period Baroque Period

Accomodation,Development,

and application Breakthrough

1928 196419231900 Present

(Periodization according to J. Evans, Introduction to "Quantum Mechanics at the Crossroads", Springer, Berlin 2007.)

Balmer

1886

Einstein

1905

Rutherford

1911

Bohr

1913

Uhlenbeckand

Goudsmit

1925

Sommerfeld

1916

Planck

1900

Selected milestones in the development of modern physics

Optical spectra

Iodine

Nitrogen

Hydrogen

Joseph vonFraunhofer1787 - 1826

Balmer’s Contribution

Johann Balmer1825 - 1898

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Spectral Series

Regularity

S P D F

TermsJohannes Rydberg

1854 - 1919Walter Ritz1878 - 1909

Max Planck1858 - 1947

Max Planck and the introduction of the quantum

• In 1900 Max Planck explained the 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).

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Planck assumed the radiation was at equilibrium with vibrating charges in the walls of the black box.

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.

• Emission of an electron takes place only afterthe electron has absorbed all the energy of the photon.

Albert Einstein1879 - 1955

Evolution of atom models

J.J Thomson1898 1908

Louis de Broglie 1923

Rutherford and Bohr1911 1913

Schrödinger 1926

Rutherford and the nucleus

Hans Geiger1882 - 1945

Ernest Marsden1889 - 1970

Ernest Rutherford1871 - 1937

• 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

• First disintegration of nuclei using accelerators (Cockroft and Walton)

$100 New Zealand Banknote

Description of Rutherford experiment

The few high angle scatterings showed the nucleus must be very small.

Niels Bohr

Niels Bohr1885 - 1962

• 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

• 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

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Sommerfeld elliptic orbits

Arnold Sommerfeld1868 - 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.

Alfred Landé1888 - 1976

2S1/2 3P0 2D3/2 3F2

• The introduction of semi-integer quantum numbers (1921) came before the introduction of spin (1925)

De Broglie matter wave - explanation of quantization

Louis de Broglie1892 - 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 pulsesJ. 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 near-circular 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)

p, n

ΔΣ

η

ω

π

ρ

Ξ

Similarities between the old quantum theory and particle physics

• The elementary particles can be seen as forming a spectrum in mass or energy.

• Regularities are found to be associated with this ‘spectrum’.

• Instead of multple levels due to spin there are isospin multiplets.

• 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).