268 
pressing the probability of such excitation occurring in 
such a collision. 
The mean free path l» of a particle of type 1, between 
collisions with particles of type 2, is of the order 1/n2Sjp, 
where Sj. is the cross section for the type of collision 
(elastic or otherwise), and m2 is the number of particles 
of type 2 per cubic centimetre of the gas. If V, is the 
mean speed of the particles of type 1, the corresponding 
collision-interval ty is l»/V1, and the mean collision- 
frequency v2 1s 1/t»2. The number of the collisions per 
cubic centimetre per second is 2, which equals 
VianyneSi Or ayNyN2, where ay = ViSi2; aw depends 
on J’, the absolute temperature, through V, (both 
directly and in Sj2), which is proportional to (T/m)”. 
Whether, in a gas contaiming excited particles, de- 
excitation occurs mainly by collision or by radiation 
depends on whether the lifetime 7’ of the excited state 
is greater or less than the collision interval t:. The 
greater the height in the atmosphere, and therefore the 
smaller the values of m; and ne, the more likely are the 
excited particles to emit their excess energy spon- 
taneously, with radiation. For example, the collision 
frequency of electrons in the D-layer of the ionosphere 
has lately been estimated to be 1.5 X 108 at 91.7 km 
height and 2.8 X 10° at 86.3 km (giving a scale height 
Hy, at this level, of 8.5 km). The collision frequency 
of atomic particles in the same region is likely to be 
smaller by perhaps two powers of ten, so that de-ex- 
citation by allowed transitions (such as those that give 
the yellow lines of sodium) would be little reduced by 
collisions, whereas atoms of oxygen in their metastable 
states 1D and 1S would not radiate appreciably at this 
level. 
14. Kinetic Energy of Particles of a Gas at Absolute 
Temperature 7. In a gas in thermal equilibrium at the 
absolute temperature 7’, the distribution of velocities 
for each type of particle (mass m, number n per cubic 
centimetre) is given by Maxwell’s formula, 
3/2 
= m —m(U2 + v2 + W2)/2k7 TaV, 5 
dn nN 7 e dUdVdW; 
dn is the number of these particles, per cubic centimetre, 
whose velocity components U, V, and W (relative to the 
mean motion, if any, of the gas) lie within the ranges 
U to U + dU, V to V + aV, W to W + dW. 
Hence in terms of the speed v of a particle (where v? = 
U? + V? + W?), and its translatory kinetic energy H 
m 3/2 ‘ 
— PUP 
— eg PE? tdy 
TT 
aie ‘a CE Pag 
Va \kT ; 
giving the number of particles dn per cubic centimetre 
with speed between v and v + dv, or energy between H 
and H + d#. The last formula does not contain m, 
whence it appears that the mean # for particles of any 
mass is the same, and equal to (34)k7' ergs, where i 
denotes Boltzmann’s constant; the energy per mole is 
THE UPPER ATMOSPHERE 
NE, or (34)RT calories, if the gas constant R is ex- 
pressed in calories per degree per mole (its value then 
being 1.986); see § 11. 
Table I gives the energy Hr in ergs and electron volts, 
and also, in the last column, its value per mole (VE 7) 
Tassie I. Mpan TrRansuatory Kinetic Enercy AT Various 
TEMPERATURES 
T 104 Ep ergs Er ev NE? cal 
deg K per particle per particle per mole 
200 4.1 0.026 596 
300 6.2 0.039 894 
400 8.3 0.052 1192 
500 10.4 0.065 1490 
750 15.5 0.097 2235 
1000 20.7 0.129 2980 
1500 31.1 0.194 4470 
expressed in calories, for 7’ from 200K to 1500K (the 
range which is of interest for the upper atmosphere). 
For particles of mass m, the mean square 7? of the speed 
(2H 7/m), and the mean speed 2, are given by 
vy = 3kT/m, 0 = (80?/3mr)2 = 0.921+/p. 
The fraction of particles (of whatever mass) whose 
energy is fH 7 or more is 
D) i ea 
Las (= GP Ate | cue a), 
Vir x0 
where xj = (36)f. This fraction is tabulated. For f = 5 
the fraction is 0.00182. 
Even at the highest temperature given in Table I, 
E is too small to produce appreciable excitation (and 
still less dissociation or ionization) by impact; and the 
fraction of the particles that have an energy of 1 ev is 
likewise very small, even at 1500K. It is not an entirely 
negligible fraction, however, and the few particles of 
high energy may have some small influence in deter- 
mining the state of the upper atmosphere. In particular, 
they will excite rotation, detectable in absorption spec- 
tra, which if obtained from high rockets may give some 
information concerning the temperature of the upper 
atmosphere. 
15. Dissociation and Ionization in the Upper At- 
mosphere. A particle can be divided mto two (thus 
being dissociated or ionized) either by radiation or by 
impact. Hach quantum of radiation absorbed, of appro- 
priate frequency » and energy hv, divides one particle, 
so that the rate of production of the separate compo- 
nent particles per cubic centimetre per second is equal 
to the rate of absorption gq of quanta, and is a function 
of the height, as illustrated for monochromatic absorp- 
tion in an exponential atmosphere in § 11. The process 
of division by absorption of radiation is called photolysis. 
The energy necessary for ionization from the neutral 
state is rather high for most of the gases of the atmos- 
4. A molecular particle without rotational energy is not 
set in gentle rotation by the impact of another particle, how- 
ever well directed, unless the transferable kinetic energy (allow- 
ing for conservation of momentum as well as of energy) at least 
equals the minimum rotational excitation energy. (See §4) 
