Modelos de la Cadena de Proveeduría

While Einstein’s paper is couched in terms of light quanta, one can pursue the general idea of light behaving in the way Einstein describes without being

committed to their existence. As part of my analysis here, I wish to draw special attention to the fact that the purpose of Millikan’s 1916 paper was not to defend or vindicate Einstein’s light quanta hypothesis: instead, it was to use experiments on photoelectric phenomena to determine the value of h with as high a precision as possible. This fact has been recognised by several historians of science, most recently perhaps by Allan Franklin (2013) and Roger Stuewer (2014), and is a significant facet of an account of the pursuit of a quantum theory. We will see that Millikan’s determination of the value of h required several steps. One step in particular provided almost conclusive proof that the relationship betweenV and ν

was exactly the linear relationship that Einstein had predicted in 1905. Millikan outlines five experimentally verifiable relationships contained in Einstein’s photoelectric equation, Equation 3.1. The most important ones for our purposes are the following:

1. There is a linear relation between V and ν.

2. dV

dν, or the slope of the V-ν line is numerically equal to h/e.

3. At the critical frequency ν0 at which v = 0, p=hν0, i.e. that the intercept of the V-ν line on the ν axis is the lowest frequency at which the metal in question can be photoelectrically active. (1916, p. 356)

He first discusses previous experiments on the photoelectric effect. These were both experimentally less reliable, and focused on a limited number of wavelengths, such that it was impossible to draw confident conclusions about the relationships between experimental values. In fact, several experiments attempting to determine the numerical value of Planck’s constant disagreed about the correct value

(Franklin, 2013, p. 577). Millikan’s group developed an accurate way to measure the photoelectric effect for a much larger range of wavelengths than was previously possible. He conducted experiments on several photoelectric materials and reported his results on the alkali metals sodium and lithium.

The determination of h proceeded as follows. First, experiments were performed in order to determine the potential difference required to stop all photoelectric emission for a particular frequency of light ν on a sodium metal surface. This was

Figure 3.1: Graph from Millikan (1916), p. 373

repeated for several values of ν. This value was not measured directly: for any given

ν, different voltages were applied to the experimental apparatus, and the resulting photocurrent was observed. Several of these observations yielded enough data to graph a line of best fit, whose potential-difference intercept was then determined. These intercept values were plotted on a V-ν graph in order to determine the general type of relation, which turned out to be clearly linear, as demonstrated in Figure 3.1.

Setting the slope of this line to h/e, and using his previously determined value for e, Millikan was able to calculate a value for h, which was 6.56×10−27_.

It was necessary to conduct this part of the experiment in a non-perfect vacuum as the observations had to be taken over a long period of time, and in the best achievable vacuum the values of some observables changed drastically after a short initial period. However, higher quality data could be obtained by taking a small number of observations in the best achievable vacuum. Thus, Millikan then adjusted the experiment so that he was able to take measurements for two different

frequencies of light in the highest attainable vacuum. Having already clearly established the linear relationship betweenV and ν using several data points, Millikan used this new data to determine the slope of the line in an alternative way. The mean value from these observations yielded a value of h= 6.569×10−27_erg·sec with an error of no more than .5 percent.

He also reported on similar experiments performed on lithium metal which yielded a mean value of h= 6.584×10−27_{erg·sec (p. 376, typo corrected), with an} uncertainty as much as 1 percent. Finally, Millikan calculates the value of h using the same method as Planck’s original calculation, but using more recent

experimental and theoretical values of the necessary variables since he estimates that Planck’s original calculation contained an uncertainty of at least 8 percent. This yielded a value of h= 6.57×10−27_erg·sec.

The above summary shows very clearly that Millikan’s main concern was the confirmation of Einstein’s equation expressing the relation between frequency and potential difference in the photoelectric effect, and the subsequent measurement of

h. This was not an experiment designed to test the light quanta hypothesis. He characterizes the inquiry as one that would allow him to “assert whether or not Planck’s h actually appeared in photoelectric phenomena as it has been usually assumed for ten years to do” (Millikan, 1916, p. 360). He also discusses the work of scientists such as Hughes, Richardson and Compton in terms of their determinations of h. Thus, we can infer that in Millikan’s view, what scientists were really able to take away from Einstein’s 1905 paper was the applicability of the parameter h to a new domain based on Equation 3.1, which guided the research programs on the photoelectric effect for the next decade.