# Rays of Positive Electricity and Their Application to Chemical Analyses/Doppler Effect Shown by the Positive Rays

Before the methods described In the earlier part of this book had been fully developed. Stark$^1$ had discovered a property of the positive rays which Is of great Importance In connexion with the origin of spectra, and Incidentally has led to results which have confirmed some of those obtained by the newer methods.
Stark's discovery resulted from the spectroscopic examination of the light produced by the positive rays passing through a gas at a pressure comparable with .1 mm. of mercury, a very much higher pressure than that used In the majority of the experiments with the photographic plate and the willemite screen. The stream of rays passing through a perforated cathode produces at such pressures in the gas behind the cathode considerable luminosity. Stark examined this luminosity when the gas was hydrogen with a spectroscope: (1) when the line of sight was at right angles to the direction of the rays. (2) When the line of sight was approximately In the direction of the rays. In the first case he found that the series lines for hydrogen were in their normal positions. In the second, however, he found that though there were lines In the normal positions, these lines were broadened out towards the violet end of the spectrum when the positive particles were approaching the spectroscope and towards the red end when they were receding away from it, indicating that some though not all of the systems emitting these lines were moving in the direction of the rays with velocities sufficient to give an appreciable Döppler effect. A closer examination of these lines brought out some interesting details which are illustrated In Fig. 45, Plate IV., taken from a photograph by Stark of the hydrogen line Hγ. It will be noticed that though the displaced line is broadened out into a band, this band does not begin at the undisplaced position of the line, but is separated from it by a finite distance. The alteration Δλ in the wave length λ of a line given out by a source moving towards the observer with a velocity v is by Doppler's principle given by the equation
    ${\frac {\Delta \lambda }{\lambda }}={\frac {v}{c}}.$
where c is the velocity of light. In the case of these small displacements we may take, where we are dealing with one line in the spectrum, Δλ as proportional to the displacement of the line, and we may also use this equation to determine v the velocity of the particle emitting the line. The fact that the fine line is displaced into a broad band shows that these velocities range over somewhat widely separated limits: this is quite in accordance with the results indicated by the photographs of the positive rays when deflected by electric arid magnetic forces. We saw that the parabolic arcs were of considerable length, and therefore were produced by particles moving with a wide range of velocities. The dark space between the undisplaced line and the band indicates that the moving particles do not give out the lines unless the velocity exceeds a certain value. According to Stark and Steubing$^2$ this limiting velocity varies with the different lines of the same element, increasing as the wave length diminishes. The limiting velocity given by these observers for the hydrogen lines are as follows: —
    H$_α$= 1.07 x 10$^7$ cm./sec. H$_β$ = 1.26 x10$^7$ cm, /sec.
These values are approximately proportional to the square root of the frequency of the lines. There is some difference of opinion as to whether this limiting velocity does or does not depend upon the frequency of the light Paschen$^3$ came to the conclusion that it was the same for all the hydrogen lines. This velocity is small compared with the average velocity of the positive rays of hydrogen; it corresponds to a fall through a potential difference of less than 100 volts. It Is comparable In value with that which the mercury atom acquired In many of the experiments represented by the preceding photographs, when It had possessed one but only one charge throughout Its journey through the discharge tube. The maximum displacement of the line depends to some extent on the potential difference between the terminals of the discharge tube; but It does not increase nearly so quickly as the square root of that potential difference, as we should expect If even the most rapidly moving particles could give out the line: the relation between the displacement and the potential difference Is given In the following table due to Stark and Steubing.$^4$ In this table r is the ratio of the kinetic energy of a particle moving with a velocity v calculated by the Doppler formula (p. 90) to the kinetic energy the particle would possess if It fell when carrying one charge through the potential difference between the terminals of the discharge tube.
    Potential Difference in Volts. r. 390 .907 555 .824 600 .716 1200 .622 3000 .358 4000 .309 4000 .402 7000 .274
Stark indeed suggests that his observations are compatible with the view that the deflections approach a limit corresponding to a velocity about 1.5 x 10$^8$ cm./sec. and do not exceed this however large the potential difference between the terminals in the discharge tube may be. The distribution of intensity in the displaced line is very complicated and seems to be affected by the purity of the gas as well as by the potential difference between the terminals in the discharge tube. Paschen$^5$ was the first to observe that there are in some cases two maxima of intensity in the displaced line, and this has been confirmed by the experiments of Stark and Steubing$^6$ and of Strasser.$^7$ The distribution of energy determined by Hartmann's microphotometer of the H$_γ$ line in very pure hydrogen is shown in Fig. 46, taken from Strasser's paper. The first peak represents the intensity of the undeflected line, the other two the intensities of the deflected. Gehrcke and Reichenheim$^8$ have suggested that the atom and the molecule of hydrogen give out the same line spectrum and that the most deflected maximum is due to the atoms, the other to the molecules. If the atom and the molecule acquired the same kinetic energy by falling through the potential difference between the terminals of the discharge tube, the velocity of the atom would be ${\sqrt {2}}$ times that of the molecule and Gehrcke and Reichenheim found in the plates that came under their observation that the ratio of the dis- placements of the two maxima was approximately equal to ${\sqrt {2}}$. This, however, does not seem by any means always to be the case, as the following table, taken from a paper by Stark,$^9$ of the results obtained by different observers, shows.

## Ratio of Displacements of the Two Maxima

    Observer. 1.75 Stark and Steubing 1.65 Paschen 1.58 " 1.50 Stark and Steubing 1.63 Paschen 1.45 Strasser 1.40 Strasser 1.37 Stark and Steubing
The photographs taken of the positive rays under electric and magnetic forces show also that in certain cases the velocities of the particles are grouped round certain values, for we find that some of the parabolas have a very decided beaded appearance: each bead corresponds to a group of particles moving with pretty nearly the same velocity. An example of this is shown in Fig. 17, Plate I. The intensity curve corresponding to the Doppler effect ought to have the same type of variations in intensity as these parabolas, and a beaded parabola ought to give rise to a Doppler curve with as many maxima as there are beads on the parabola. Sometimes these beads on the parabolas are quite numerous.
It is remarkable that the parabola corresponding to the atom of hydrogen is often beaded in such a way that the velocity of the particles producing one bead is to that producing the other as ${\sqrt {2}}:1$. Thus to explain the maxima in the Doppler curve with displacements in this proportion it is not necessary to assume that the molecules give out the same spectrum as the atom. The occurrence of singly charged atoms of hydrogen with velocities in this proportion of ${\sqrt {2}}$ to 1 might be accounted for in some such way as the following: the atoms with the larger velocity have been charged atoms during the whole of their career; they were atoms before they passed through the cathode and continue in this state after emerging from it; the atoms with the smaller velocity were part of a charged molecule before passing through the cathode; the molecule would only acquire a velocity$1/{\sqrt {2}}$ that of the atom. After passing through the cathode and before being deflected by the electric and magnetic fields this charged molecule breaks op into two atoms, while a the other is uncharged.
The Döppler effect we have been considering is by the "series spectrum" of hydrogen. In addition to this spectrum hydrogen gives a second spectrum containing a great number of lines, and this spectrum Is developed,, not so brightly as the series spectrum, when positive rays pass through hydrogen. Stark$^{10}$ has shown, and his results have been confirmed by Wilsar,$^{11}$ that the lines in the second spectrum of hydrogen do not show the Döppler effect with the positive rays. We infer from this that the second spectrum of hydrogen is not due to any of the constituents of the positive rays. This result illustrates the importance of this method for questions relating to the origin of spectra.
Another illustration of this is the case of oxygen. Oxygen gives a series spectrum, a spark spectrum which has not been resolved into series, and some banded spectra. All these spectra are emitted when oxygen positive rays pass through oxygen, the spark spectrum being the brightest With oxygen it is the spark lines that show the Döppler effect. Wilsar and Paschen could not detect any such effect with the series lines. Stark, however, who used very large dispersions, found the effect in some of the lines; the intensity of the displaced lines was, however, very small compared with that of the undisplaced lines, while in the spark lines the displaced intensity$^{12}$ is quite comparable with the normal intensity.
Nitrogen has a line spectrum which has not been resolved into series, and some banded spectra. The line spectrum and one of the banded spectra are found where nitrogen positive rays go through nitrogen; the banded spectrum does not show the
Döppler effect. Some of the lines in the line spectrum show it very distinctly, while it is quite absent from others (Herman, Wilsar).$^{13}$ A very interesting point about the effect in nitrogen is that even for those lines which show the effect the value of Δλ/λ is not constant. Wilsar gives the following table for the Döppler effect for some of the nitrogen lines:—
    Wave Length. Δλ/λ 5002.9 11.4 4643.4 10.35 4630.9 10.14 4530.3 10.14 3995.2 6.90
Thus the effect for the line 3995.2 is much less than for any of the others showing that the velocity of the source of this line is considerably less than that of the sources of the others. The different states in which nitrogen occurs in the positive rays are atoms with two charges, atoms with one charge, molecules with one charge, and in exceptional cases atoms with three charges and a tri-atomic molecule with one charge. If the majority of the lines were given out by the doubly charged atom and the line 3995.2 by the singly charged one we should get relative values of Δλ/λ, approximately equal to those in the preceding table.
Stark's experiments have shown that the source of the series lines is one of the constituents of the positive rays: the question is, which constituent. We have seen that in hydrogen, for example, we have positively and negatively charged atoms, as well as neutral ones: we have also positively charged and neutral molecules. There is considerable difference of opinion as to which of these is responsible for the series lines in the hydrogen spectrum. All theories concur in regarding the atom and not the molecule as the source of these lines, but according to Wien's theory the in the neutral state, while Stark maintains that the radiation Is emitted when the atom has a positive charge: according to his the lines emitted by the neutral atom are far away in the ultraviolet.
The pressures at which spectroscopic observations have been made are so high that an atom is continually passing backwards and forwards between the neutral and charged conditions. It is thus a matter of great difficulty to determine whether the atom emits the lines in one state or the other, and there Is, I think, at present no experiment which is absolutely decisive between the two views. Thus, for example, it is found that the Doppler effect is increased when the positive rays are exposed to an accelerating potential after passing through the cathode. This, however, does not prove that the particles are charged when giving out the light, for the particles which are uncharged at one time have at other times a positive charge and so would be accelerated.
Perhaps the strongest argument in favour of the radiating particles being positively charged is that in certain cases, as Reichenheim has shown, the anode rays (see p. 84) show the Döppler effect, but even this is not conclusive, as some of the positively charged particles might have been neutralized after they had acquired their high velocity under the electric field.
There is another view as to the origin of the radiation which explains in a simple way some of the characteristic properties of the Döppler effect: this is that the light, is given out by particles which have just been neutralized by union with a negatively electriied corpuscle. The corpuscle falls into the positively charged atom and the energy gained by the fall is radiated away as light. On this view the intensity of the light should vary with the number of recombinations of positive ions and negative corpuscles. Let n be at any instant the number of neutral particles per unit volume moving velocity V, p the number of positive particles moving with the same velocity, N the number of corpuscles In the tract of these particles per unit volume.
Then the number of recombinations per second will be
    $pNf(v)\,$
when f(v) is a function of v which will vanish when v Is very large, for recombination will not take place If the relative velocity of the positive particle and the corpuscle exceeds a certain value.
The number of neutral particles Ionized per second will be
    $nNF(v)\,$
where F(v) Is a function of v which vanishes when v Is very small, for If the particle is to be ionized by a collision the relative velocity of the particle and corpuscle must exceed a critical value.
When the composition of the beam of positive rays has become steady the number of ionizations must equal the number of recombinations, hence
    $pNf(v)=nNF(v)\,$
and therefore
       $={\frac {(p+n)Nf(v)F(v)}{f(v)+F(v)}}\,$
Since f(v)=0 when v = infinity and F(v) = 0 when v=0, f(v)F(v) will have a maximum for a certain value of v which will not however depend on the potential difference between the electrodes In the discharge tube. The factor p+n, the total number of positive rays charged or neutral whose velocity is v will also be a function of v and this function will depend upon the value of E, the potential difference between the electrodes In the discharge tube, for evidently if E increases, the value of v for which p+n is a maximum will increase too. On the view we are considering, the intensity of the light showing a Döppler effect corresponding to the value v will beproportional to the number of recombinations of positive ions moving with this velocity with negatively electrified corpuscles. It will thus be proportional to pNf(v) which we have seen is equal to
       $(p+n){\Bigg \{\frac {f(v)F(v)}{f(v)+F(v)}}{\Bigg \}}N\,$
The second factor in this expression
       ${\frac {f(v)F(v)}{f(v)+F(v)}}$
has its maximum value for a value of v which does not depend upon the potential difference: the other factor (p + n) does depend upon this potential difference. Thus the value of v for which the product of these factors is a maximum will depend to some extent on E, but since the value of v which makes one of the factors a maximum is quite independent of E we should expect that the variation with E of the velocity which makes the product a maximum would be smaller than the variation in the average velocity of the particles in the positive rays.
Again since F{v) vanishes when v is less than a certain value v$_0$ there will be no light showing a Döppler effect corresponding to a velocity less than v$_0$, thus there will be a dark space between the original line and the displaced lines. This also is in accordance with the observations. Since f{v) vanishes when v is greater than a certain value v, there will be no Doppler effect showing a greater displacement than that corresponding to v. Though it has not perhaps been absolutely proved there are strong indications that the Doppler effect cannot be increased beyond a certain definite value, however large the potential applied to the discharge tube may be.
The spectroscopy of the positive rays suggests some very interesting questions, as, for example, what kind of light do the molecules emit? In the positive rays in hydrogen the molecules frequently outnumber the atoms, but no radiation that can be attributed to the molecules has yet been detected.The spectrum of hydrogen is there, but as it does not show the Döppler effect it cannot be due to the molecules. It would seem as if the molecules must either give rise to a continuous spectrum or else to one in the infra red.
As the second spectrum of hydrogen is present when the positive rays pass through a gas, but does not show any displacement, it must arise from some process in which the moving particles do not take part, such for example as the combination of a positive atom with a negative one (not with a corpuscle) to form a neutral molecule.
Stark$^{14}$ has detected by the increased Döppler effect lines due to the doubly and triply charged atoms of mercury and to the doubly charged atom of helium. He finds that the lines given out by the multiply charged atoms belong to different series in Faschen and Runge's classification from those given out by atoms with only one charge.
When positive rays produced in a gas A pass through a gas B the spectra of both A and B are given out: Wilsar, "Phys. Zeitschr.," 12, p. 1091, and Fulcher (ibid. 13, p. 224), have shown that all the lines of A are displaced while all those of B are in their normal position. A bibliography of the Döppler effect in the Positive Rays has recently been published by Fulcher, " Jahrb. d. Radioaktivitat," X, p. 82, 1913.
$^1$ Stark, "Physik. Zeitschr.," 6, p. 892, 1905. "Ann. d. Phys.," XXI, p. 451, 1906.
$^2$ "Ann. der. Phys.," 28, p. 974.
$^3$ "Ann. der Phys.," 27, p. 599.
$^4$ Ibid., 28, p. 974.
$^5$ "Ann. der Phys.," 23, p. 247, 1907,
$^6$ Ibid., 28, 978.
$^7$ Ibid., 31, 890, 1910
$^8$" Verh. d. Deutsch. Phys. Ges.," 12, p. 414, 1910.
$^9$ Ibid., 12, p. 711,1910.?
$^{10}$ Stark, " Ann. der Phys.," 21, p. 425, 1906.
$^{11}$ "Ann. der Phys.," 39, p. 1251,1912.
$^{12}$ Paschen, "Ann. der Phys.," 23, p. 261, 1907.
$^{13}$ "Phys. Zeit.," 7, p. 568,1906.
$^{14}$ "Ann, der Phys.," XL, p. 499, 1913 ; XLII, p. 241, 1913.