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Unravelling the Mystery of the Atomic Nucleus pp 89–162Cite as

Quantum Mechanics: The Unavoidable Path

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Abstract

In a lecture delivered on February 16, 1901, “on the molecular hypothesis,” Jean Perrin explained:

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Notes

  1. 1.

    See p. 52.

  2. 2.

    Blue has a wavelength roughly two times smaller than red.

  3. 3.

    He finds that the curve is a function of the product λT of the wavelength of the radiation multiplied by the temperature T.

  4. 4.

    His exponential law was: \(\rho (\nu,T) = \alpha {\nu }^{3}{\mathrm{e}}^{-\beta \nu /T}\), where ν is the frequency of the radiation. The constants α and β are chosen so as to fit the experimental data and they are not given physical meaning.

  5. 5.

    The longest wavelength of visible light is in the red and equal to about 0.8 μm. The micrometer (μ)m is equal to one thousandth of a millimeter.

  6. 6.

    A temperature of 300K corresponds to \(300 - 273 = 27\) ∘C, which is the temperature of a hot summer day.

  7. 7.

    The formula of Raleigh is \(\rho= \frac{8\pi {\nu }^{2}} {{c}^{3}} kT\), where ν is the frequency, k Boltzmann’s constant, and c the speed of light.

  8. 8.

    Meaning that he did not hold a chair.

  9. 9.

    For one mole of a perfect gas, that is, for 22.4 l at a temperature of 20∘C at atmospheric pressure, the constant R, multiplied by the absolute temperature T (which is the usual measured temperature plus 273∘C), is equal to the pressure of the gas multiplied by its volume.

  10. 10.

    See p. 69.

  11. 11.

    The theory of radiation and quanta.

  12. 12.

    See p. 54.

  13. 13.

    See p. 133.

  14. 14.

    See p. 56.

  15. 15.

    With the presently known values of the mass and charge of the electron, the value of Rydberg’s constant is 3.2899 ×1015s−1.

  16. 16.

    See p. 24.

  17. 17.

    Here ℏ stands for h∕2π. See below p. 50.

  18. 18.

    By purposely crazy reasoning, they “derived” the formula \({T}_{0} = -(2/\alpha- 1)\) degrees.

  19. 19.

    See p. 59.

  20. 20.

    There exist 15 elements which are called “rare earths” or lanthanides. Their atomic number range from 57 to 71: lanthanum, cerium, praseodymium, neodymium, promethium, samarium, europium, gadolinium, terbium, dysprosium, holmium, erbium, thulium, ytterbium, and lutetium. Promethium was the last to be identified in 1947.

  21. 21.

    Recall that orbits with one, two, three… quanta are orbits whose principal quantum number n is one, two, three…. The number n determines approximately the size of the orbit, and its quantum number k the elongation (eccentricity) of the orbit. See p. 28.

  22. 22.

    See p. 32.

  23. 23.

    Today, the town is in Poland and it is called Wrocław.

  24. 24.

    See p. 11.

  25. 25.

    However, the name of Einstein was not mentioned in Compton’s paper.

  26. 26.

    The factor g is still used today. It is no longer a mystery and it still called the Landé factor.

  27. 27.

    When n = 2, k can acquire the two values k = 1,2; when k = 1, only the value m = 0 is allowed; when k = 2, the three values \(m = -1\), m = 0 and m = 1 are allowed; all together, when n = 2, there are four sets of allowed values for k and m and for each set, two values of m 2, which amounts to a total of eight.

  28. 28.

    The following account is, for the most part, taken from the introduction, by Klaus Stolzenburg, to the Volume 5 of the Collected Works of Niels Bohr.

  29. 29.

    See p. 15.

  30. 30.

    The word photon was proposed in 1926 by the American physicist Gilbert Lewis [93]. It was quickly adopted by physicists.

  31. 31.

    See p. 43.

  32. 32.

    That is the content of Newton’s famous equation f = ma where f is the force acting on the electron with a mass m. The electron undergoes an acceleration a.

  33. 33.

    We will describe later (p. 222) the Wilson chamber, in which an electrically charged particle, such as an electron, induces the condensation of small water droplets, a mist, which gives a material and visible form to the particle trajectory, in a fashion similar to the one of the white trail which is often observed behind high altitude jet planes in the sky.

  34. 34.

    See the footnote (p. 148) and the description of the Wilson cloud chamber( p. 222).

  35. 35.

    The momentum p of the electron is equal to the product mv of its mass m by it velocity v.

  36. 36.

    See p. 327–331.

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Fernandez, B. (2013). Quantum Mechanics: The Unavoidable Path. In: Unravelling the Mystery of the Atomic Nucleus. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4181-6_3

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