cases considered the term is 1014 to 1015, and therefore

hv

is large compared with unity. Consequently N, reduces kT to N and (KT-1) to ehkT ̧ Hence we obtain finally for the velocity constant of unimolecular decomposition :

This equation differs from that of Dushman only in the factor Pm which may be greater or less than unity. For

Pn

Bohr orbits in the generalized Sommerfeld sense, Pm would

Pm
Pn

be greater than p, but in no case would be a large numerical factor.

It will be obvious that the result obtained depends primarily on the assumption that A-that is, that the life of a stationary state m is equal, in the absence of radiation, to the period which characterizes the transitions nm. The corresponding rate of absorption from a radiation field is very much greater than that given by classical electrodynamics. It may be noted that the expression for this rate does not contain in itself any of the properties of the absorbing system except the frequency v, and even this is only associated with the system for a particular transition.

The law of spontaneous emission should be that which governs radioactive transformations, unless these are dependent in some way on a very penetrating external radiation with 1021, as proposed by Perrin (Ann. Phys. xi. p. 5, 1919). This would make a radioactive change. essentially a photochemical process as distinct from a thermal process considered above. (For a discussion of this distinction, ef. Lewis and McKeown, loc. cit.) It can, of course, be argued that since radioactive changes are never instantaneous but obey the unimolecular law some preliminary species of activation is necessary, whether this be dependent on the action of radiation in the Perrin sense, or merely on some fortuitous spatial orientation (independent of temperature) in the nucleus which decomposes.

Summary.

Applying Einstein's concept of the mutual action of radiation and matter, and making use of a postulate in

this connexion advanced by Christiansen, the following expression has been obtained for the velocity constant of a unimolecular chemical change:

proposed by Dushman, and which has been shown by him to be in agreement with existing experimental data.

Department of Physical Chemistry,
University of Liverpool.

XXXII. Note on the Velocity of a Unimolecular Chemical Reaction. By W. C. M. LEWIS *.

the basis of the expression employed by Planck for the rate of absorption of radiant energy by an oscillator, the act of absorption being regarded as continuous, the author pointed out more than three years ago (Phil. Mag. [6] xxxix. p. 26, 1920) that an expression for the velocity constant of a unimolecular change could be obtained which involved, amongst other quantities, a refractive index term.

If the refractive index term is identified with that of a gaseous system as a whole, its value is practically unity. On this basis the expression for the velocity constant was found to lead to a value which was only one ten-millionth of that actually observed. Lewis and McKeown (Journ. Amer. Chem. Soc. xliii. p. 1288, 1921) attempted to account for this discrepancy by assuming a greatly increased value for the actual refractive index. of the individual molecules, in semi-quantitative agreement with an earlier conclusion of Lamb regarding the dielectric constant of a molecule (Trans. Camb. Phil. Soc. xviii. p. 348, 1900).

It was felt, however, that to account for the discrepancy on the basis of the refractive index within the molecule was physically far from satisfactory. The experimental facts lead one to the conclusion-provided absorption of radiation is the physical cause of chemical changethat Planck's expression for the rate of absorption by an

* Communicated by the Author.

oscillator gives a value which is far too low, unless we can assume either that the radiation density exhibits fluctuations and is locally condensed close to and around the individual molecules of every material substance, or that the oscillator is capable of drawing upon the radiation present in a volume which is great compared with the magnitude which might be attributed to the oscillator itself *.

The latter possibility is attractive in view of a result obtained by the late Lord Rayleigh (Phil. Mag. xxxii. p. 188, 1916) on the rate of absorption by a symmetrical oscillator. It is doubtful whether it is legitimate to use this type of oscillator in the present case. Assuming that it is justifiable, we can make use of Lord Rayleigh's conclusion-namely, that such an oscillator in a given time will absorb the energy which passes through an comparable with A/T, where X is the wave-length of the radiation concerned in the chemical change. This would mean that in one second the amount of radiation absorbed x2 c is that which would be present in a volume

π n

area

where

e is the velocity of light in vacuo and n the average refractive index of the system for this wave-length. The radiation density being udv, the amount of energy absorbed by such an oscillator per second is given by

(It will be observed that the refractive index term has vanished.) For frequencies in the short infra-red, visible, and ultra-violet (which includes the chemically significant region), the expression becomes

8hv. e-hv, kT dv.

Dividing this by hy, we obtain the number of molecules each of which absorbs one quantum of the frequency v during one second, and consequently we obtain for the unimolecular velocity constant the expression

where dy represents the width of the band or range of

* In the long run these two possibilities may not be very different.

frequencies which the molecule is capable of absorbing round about frequency v.

The width of a band is usually defined as that spectral region over which the absorption coefficient falls to one-half of the maximum value which it possesses at the head or optical centre of the band (Ribaud, Annales de Physique, xii. p. 188, 1919). Ribaud (Comptes Rend. clxxi. p. 1134, 1920) considers that the width of a band (as distinct from that of a line) is defined solely by the position of the head of the band at which absorption occurs. Thus for band heads at 270 μμ 500 μμ, Ribaud finds the and 3.3 μ corresponding widths to be 42 μμ, 77 μμ, and 720 μμ respectively. As a first approximation, therefore, we can write λ=6dλ or dv=0·17v. Equation (1) would then take the form

Owing to the approximate nature of the initial assumption -namely, that the oscillator absorbs the energy which passes through an area comparable with X/7,-it follows that no precision can be attributed to the numerical term (8×0.17). It would appear, however, that the expression (2) is capable of giving values comparable with those given by the empirical equation of Dushman, namely kv.e-hv/kT, which, for the case of gaseous systems and for dissolved gases, has been found to accord fairly well with the experimental values, although it should be pointed out that very considerable discrepancies are found in the cases in which a non-volatile solute decomposes in solution in a unimolecular manner.

Department of Physical Chemistry,
University of Liverpool.

XXXIII. Note on the Chemical Constants of Diatomic Gases. By J. R. PARTINGTON, D.Sc.

IN

the Philosophical Magazine for November 1922 (vol. xliv. p. 988) I obtained an expression for the chemical constant of a diatomic gas which (equation 15 in the paper) is

log

m5/2 p2 27/2
h5

7,247/2 π

or

for the case of a molecule composed of two like atoms.

*Communicated by the Author.

I now find that an expression reducing to the above had been found by the late Dr. Sackur by a slightly different method. In a paper in the Annalen der Physik, vol. xl. p. 98 (1913), he gives an expression which, when applied to the case considered, reduces to

C 12.548+2.5 log M + 2 log r

=

and on p. 95 he obtains an expression (when the atoms are identical),

which differs only by the addition of log, 2 from (1), since the case investigated by Dr. Sackur was that mentioned on p. 993 of my paper, where it is stated that log, 2 must be added. (Slightly different values for k and were used by Dr. Sackur.)

I am still of the opinion that for a molecule composed of two identical atoms, the expression given by Dr. Sackur is in excess of the correct value by log, 2.

In my paper I also referred to the possibility of quantizing the angular momentum instead of the rotational energy; the latter would follow from the considerations advanced by Bjerrum it is a very simple matter to modify the calculation, taking the expression v=nh | 42I instead of v=nh | 2π2I.

XXXIV. On the Mechanism of the Electric Are.

To the Editors of the Philosophical Magazine.

DEAR SIRS,-

ITH reference to a recent contribution on the electric

WITH by Professor Duffield (June 1923) I am sorry to

find that he and I are still in disagreement in the interpretation of the results he obtained. He criticises my use of deductions on the ionic distribution in the body of are in the discussion of what takes place very near to the cathode. This criticism would be justifiable if we were concerned in his theory only with the repulsion of the cathode. But he explains the repulsion of the anode by postulating that electrons are projected from the cathode and communicate their momentum to the anode. Mr. Beer and I searched for them directly *Ber. Deutsch. Phys. Ges. xvi. p. 640 (1914).