Abstract
A detailed of pursuit in the history of β decay experiments in the early twentieth century. As noted above, our major study will deal with the pursuit and development of these experiments on β decay, because in this case theory played only a minor role as opposed to the other episodes that we deal with where theory played a more important role.
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Notes
- 1.
- 2.
By the “ordinary absorption law” Rutherford meant that the intensity of the radiation “diminishes in a geometrical progression with the thickness of metal... i.e. according to an ordinary absorption law.” See Rutherford (1899, p. 115).
- 3.
- 4.
For confirmation on this continuity of design see Kohlrausch (1928, pp. 202–203).
- 5.
The origin of this figure is uncertain because none of the references to Becquerel cited at Kohlrausch (1928, p. 198) contains this figure.
- 6.
See Jensen (2000, p. 4).
- 7.
- 8.
- 9.
- 10.
While Schmidt’s publication does not include an illustration of his apparatus, his description at Schmidt (1906, p. 764) is consistent with Fig. 2.5 which occurs at Rutherford (1904, p. 82) and again at Rutherford (1913, p. 106) where the apparatus is described as “very convenient for many measurements in radio-activity.”
- 11.
Translation by Jensen (2000, p. 8).
- 12.
For a detailed explanation of how such a magnetic field works to segregate velocities see Rutherford (1913, pp. 72–75).
- 13.
Translation at Jensen (2000, p. 11).
- 14.
We’ve already discussed Bragg’s warning about the effect of scattering, but for more on the then contemporary understanding see Rutherford (1913, pp. 212–222) who pointedly noted that: “It would be very convenient to call the rays which are turned back on the side of incidence the reflected rays, and those which pass through the plate the transmitted rays. In using the term ‘reflected,’ however, it must be remembered that the phenomenon has no analogy with light, but that the reflected rays consist of the primary β particles which have been so scattered by the atoms of matter that they emerge again in all directions” (p. 213).
- 15.
We’ll review the mathematical description of linear and exponential absorption, and absorption coefficients, when we get to Wilson’s 1909 experiment.
- 16.
Translation by Jensen (2000, p. 13).
- 17.
- 18.
This feature mirrors what was an accepted feature of alpha particles.
- 19.
This meant that Schmidt’s ionization-field strength curve (when no absorbing material was involved) had to be seen as a secondary phenomenon and not as indicative of an underlying β-ray spectrum.
- 20.
Translation by Jensen (2000, p. 16).
- 21.
- 22.
Wilson cites (Hahn & Meitner, 1908a, p. 321) as an example of those who have assumed this.
- 23.
Wilson notes that “[t]he field was found to be practically uniform” (p. 614).
- 24.
Actually, this calculation is somewhat more complicated because it requires the relativistic correction for the increase in mass at very high speeds. See Wilson (1909, pp. 617–618).
- 25.
Wilson would later go on to demonstrate this experimentally at Gray and Wilson (1910).
- 26.
Wilson briefly references such theories at (p. 625).
- 27.
This explains the lack of specific data points for curves b and c since those curves incorporate Wilson’s earlier results showing linear absorption.
- 28.
What Wilson is referring to here is, as we noted earlier, that Schmidt had expressly noted that his data did not support a pure exponential law of absorption for RaE and were not otherwise explainable in terms of a sum of exponential functions.
- 29.
See Crowther (1910, pp. 443–444) for a further (but only qualitative) review of the various ways in which non-homogeneous rays could enter through an aperture of finite size.
- 30.
All translations of Hahn and Meitner’s response to Wilson are by the authors.
- 31.
It is surprising to see Hahn and Meitner appeal to a difference between slower and faster β-rays given their “working hypothesis” that β-rays emitted from pure substances are all of the same velocity and suffer no decrease in velocity when passing through absorbing media. What they may have had in mind is some combination of a relative lack of parallelism (and thus a difference in velocity as opposed to speed) because of the finite aperture size, coupled with other secondary effects such as scatter.
- 32.
Actually, there’s more than just a notational convenience involved here, since the Hahn-Meitner scheme is also a simplified account of a more complex underlying phenomena. Just how much more complex will be seen when we consider (Wilson, 1910).
- 33.
Hahn and Meitner add the caveat that “[o]nly when you have used so much aluminum that this condition is no longer fulfilled because of excessive absorption, does a shift of the maximum occur, towards the side of the stronger field” (p. 950).
- 34.
Wilson wrote his response in German and all translations that response is by the authors.
- 35.
Wilson also argued (at p. 103) against Hahn and Meitner’s claim that “[i]t goes without saying that the maximum for [the curves b and c] moves to the side of the stronger fields.” But for current purposes we need not delve further into those complexities.
- 36.
In this regard remember that Wilson had earlier informed Hahn and Meitner, that he had recently completed new experiments where the β-rays produced “are much more homogeneous,” and which showed that linear absorption is “confirmed with even greater accuracy than under the earlier experimental conditions” (Wilson, 1910, p. 102, emphasis added).
- 37.
For the claim that this area represents the total energy produced at the data point of the curve analogous to curve a, see Wilson (1909, p. 622): “The area of this curve, then, represents the ionization we would get in the electroscope if all of the rays of all velocities were allowed... were allowed to enter together instead of being deflected into the electroscope separately by the magnetic field.”
- 38.
As restated in Wilson (1912, p. 310): “[T]he exponential law of absorption found for a beam of rays emitted by a single radioactive substance can be explained by assuming that the numbers of particles composing the beam are distributed according to some special law with respect to their velocity.”
- 39.
See also Rutherford (1913, 245–248) for other relevant experimental results.
- 40.
Wilson added: “The actual number of particles was not determined owing to the difficulty of measuring the capacity of the gold-leaf system” (p. 242).
- 41.
See Wilson (1912, p. 323) where this relationship was used as part of his explanation of why homogeneous particles became heterogeneous as they made their way through absorbing media.
- 42.
- 43.
Translation by the authors. It’s an odd fact that in this early photograph ThA is more strongly represented than ThD, whereas in later photographs, discussed below, the opposite is the case. What explains this apparent inconsistency is the fact that the rays from ThD are not as homogeneous as those from ThA and that this difference was somehow exaggerated in the early photographs.
- 44.
For an explanation of the identifying terminology for radioactive substances see Rutherford (1913, pp. 534–552).
- 45.
Because of their small size only a vertical white line is visible against an entirely black background where the vertical line is most likely the α-line and the ThD β line in close proximity. This is the case with the available digitized versions available from the Columbia, Princeton and Michigan University libraries.
- 46.
Translation by Jensen (2000, p. 27).
- 47.
Translations from this paper are by the authors.
- 48.
Note that the photographic plate had to have been oriented so as to be horizontal as it had been in the earlier experiments.
- 49.
Chadwick wrote his article in German, and all translations here are by the authors.
- 50.
Chadwick to Rutherford, 14 January 1914, cited in Jensen (2000, p. 42), emphasis added.
- 51.
One peculiarity for which we have no explanation is the fact that Chadwick did not indicate any particular data points on the graphical representation.
- 52.
There’s another factor that may have come into play here. As noted by Rutherford et al., (1930, p. 399) Chadwick’s apparatus “was the first application of the focusing method to electrical measurements” where, as noted above, this focusing method was also taken advantage of in Rutherford and Robinson (1913, p. 720). Consequently, Chadwick’s apparatus very likely had greater sensitivity than that used by Wilson. Couple this with the “relatively very low intensity” of the line spikes that Chadwick had been able to discover and it’s not surprising that Wilson and other experimenters did not detect those spikes.
- 53.
Chadwick to Hevesy, 12 March 1914 cited at Jenson (2000, p. 44), emphasis added.
- 54.
For details of the internment see Chadwick (1969, Sessions I and II).
- 55.
See Jensen (2000, pp. 56–63) for background on Ellis’ theory.
- 56.
Translation by Jensen (2000, p. 64).
- 57.
Ellis was not the only one who considered such an investigation pursuit worthy. For an extensive review of the experimental efforts with this purpose in mind see Jensen (2000, pp. 123–128).
- 58.
Translations by Jensen (2000, pp. 92–93).
- 59.
See. e.g., Chadwick and Ellis (1922, p. 276) where they argue that the “effect of stray β-radiation, arising from scattering” is “of small importance to the order of accuracy of the experiment.”
- 60.
Meitner to Ellis, 16 November 1925, cited at Jensen (2000, p. 78).
- 61.
See Jensen (2000, pp. 55–119) for an extensive account of the development of these and other theories as to the internal workings of the atoms and nuclei of radioactive substances.
- 62.
Here Ellis and Wooster made reference to Emeleus (1924, p. 400).
- 63.
- 64.
From Ellis and Wooster (1927, p. 111) citing “experiments of Mr. Madgwick carried out at the Cavendish Laboratory” (p. 120).
- 65.
Note though that the possibility of monoenergetic disintegration within the nucleus (as discussed in the 1925b paper) is not mentioned. This omission may be because the “missing energy” would be the same for monoenergetic disintegration within the nucleus as it would be for secondary causes acting on β-rays once they had escaped the nucleus.
- 66.
For a detailed description of the calorimeter see (p. 113).
- 67.
Meitner 1929 letter sent to Ellis cited in Jensen (2000, p. 130), and Pais (1977, p. 927).
- 68.
Po only produces alpha particles and moreover it was known that such particles were emitted all with the same velocity.
- 69.
Both decay periods were used in order to determine the net half-life of the Po which takes into account the contribution due to RaE decay and the radiation loss on the part of the Po. Assuming that the resulting amount of Po is proportional to the heating effect (as had been earlier assumed for the RaE), one then in effect inserts this extrapolation into Fig. 2.24 where the extrapolation shows “the heating effect due to the polonium” (p. 117).
- 70.
See pp. 118–121. While we have chosen, in the interests of economy of presentation, to skip over this material (and related appraisals of confounding factors in the experiments discussed earlier), we want to emphasize that a central feature of every experiment is an analysis of the effect of confounding factors, where this analysis typically involves experimentation on the experimental apparatus itself. Acceptance and even pursuit worthiness depend on the results of such analyses of confounding factors. We’ll go over this aspect of experimentation in more detail in our next case study.
- 71.
For more details on these improvements and on the additional efforts by Meitner and her colleagues to detect confounding causes that would result in heat leaking from the calorimeter see Jensen (2000, pp. 141–143).
- 72.
After the discovery of the neutron by Chadwick in 1932, a heavy particle that was considered to be a constituent of the nucleus, there was some confusion in the physics literature between the two particles, Chadwick’s and Pauli’s. Fermi solved the problem by christening Pauli’s particle the “neutrino,” or little neutral one.
- 73.
- 74.
At the time the accepted model of the atomic nucleus was that it consisted of protons and electrons, the only two massive particles known. In addition to the energy conservation problem in beta decay, this model also had difficulties with the stability of the nucleus, the size of nuclear magnetic moments, and the spins of several nuclei.
- 75.
Pauli’s suggestion also solved a problem associated with the spins of several nuclei. However, other problems remained. These were solved when Chadwick discovered a neutral particle with a mass approximately that of the proton. This neutron was incorporated into the model of the nucleus and used in Fermi’s theory of beta decay. For Fermi beta decay was the decay of a neutron into a proton, electron, and a neutrino. In such a three-body decay the electron is no longer required by conservation of energy and momentum to have a unique energy. For details see Franklin and Marino (2020, pp. 60–62).
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Laymon, R., Franklin, A. (2022). The Beta Decay Spectrum: Experimental Discovery and Pursuit. In: Case Studies in Experimental Physics. Synthesis Lectures on Engineering, Science, and Technology. Springer, Cham. https://doi.org/10.1007/978-3-031-12608-6_2
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