Ionizing Potentials.
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Gas
Stead & Gosling
Franck & Hertz
Davis & Goucher
Horton & Davis
Tate& Foote
Hughes & Dixon
H 2
15
II
1 1 and 15
IO-2
He
20-8
20-5
25-6
2
9
9-2
N.
17-2
7-5
17
7-7
co
15
7-2
Arg.
12-5
12
15
Ne
I6--& 20
& 22-8
H|
10-8
IO-2
Cd
8-9
Na
5'i
K
4-1
Zn
9-5
The me trons is t molecule < energy to electron, versely as energy of lar from t of the me tron in t
equal to
>st obviou lat the m )f the gas enable it If the el the squa the movi ic electroi ving elect ic molecu T
s view to take of this ionization by moving elec- aving electron comes so near to an electron in a that the latter receives from the collision enough to escape from the molecule and start as a free ectrons repel each other with forces varying in- re of the distance between them, and if T is the ig electron, and d the length of the perpendicu- i in the molecule on the initial direction of motion ron, then the energy communicated to the elec- le by its collision with the moving electron is
, where e is the charge of electricity on an elec-
d 1 ,
tron. This is on the supposition that the electron is moving so rapidly that the time while it is in close proximity to the electron in the molecule is small compared with the time of vibration of that electron; if this time is comparable with the duration of the colli- sion, the energy taken from the moving electron will be consider- ably less, and it will become vanishingly small when the duration of the collision is large compared with the time of vibration. The energy given to the electron in the molecule does not increase indefi- nitely with that of the moving molecule, for it vanishes when T is infinite as well as when T is zero; it has the maximum value when T = e 2 / In order that the electron in the molecule should receive an amount of energy Q,
If Q is the ionizing potential, 2 must be less than the value given by this expression. If n is the number of electrons in unit volume of the gas, and if the spheres with radius d described round the different electrons do not overlap, the probability that the moving electrons should come within this distance of one of them, when moving through a distance Ax, is mrd'-&x, or
nire(T/Q-i)' p
The coefficient of A* is the number of ions made per unit path by a moving electron with energy T. The maximum is when T = 2Q.
Experiments on ionization by moving electrons have been made by Kossel (Ann. der Phys. 37, p. 406) and by Mayer (ibid. 45, p. l), who found that the maximum ionization per unit path occurred when the energy of the moving electron was in the neighbourhood of 200 volts. Mayer's results are 125 for hydrogen, 130 for air, and 140 for carbon dioxide. These numbers are much greater than twice the potential at which the ionization begins, as this potential is of the order of n volts. It must be remembered, however, that, though there may be some electrons in the atom which can be ejected by 1 1 volt electrons, there may be other electrons of different types which require more energy for their expulsion, so that, as the energy of the moving electrons increases beyond the energy required to liberate these electrons, fresh sources of detachable electrons will be trapped, and these may more than counterbalance the falling off in the ionization of the more easily detached electrons. Again, some of the electrons ejected by the primary electrons may have enough energy to ionize on their own account; the total ionization may thus be increased by ionization due to the secondary electrons, and also by radiation excited by the impact of the primary electrons against the molecules of the gas.
When, as in the case of cathode rays in highly exhausted tubes or in that of the ft rays from radioactive substances, T is very large compared with Q, the number of ions produced per unit path is nreVQT, and so varies inversely as the energy of the moving elec- trons. The experiments of Glasson on ionization by cathode rays, and of Durack on that by ft particles, seem to be in accordance with this result. If we measure the number_of ions produced per centimetre in a gas at known pressure, for which we know the value
of Q, we could determine n, the number of electrons in unit vol- ume; as the pressure gives us the number of molecules, we could deduce in this way the number of electrons in each molecule.
Ionization by Moving Ions. When the moving systems are ions instead of electrons, the collision between them and the elec- trons are collisions between masses of very different magnitudes, and in consequence a very much smaller fraction of the energy of the moving body is transferred to the electron than when the colliding bodies have equal masses.
The amount of energy transferred to the electron when the moving body has a mass M is equal to :
4d 8 TV M; " 2 E 2 \K
when MZ is the mass of the electron and E the charge on the mov- ing body. When, as in the case of the collision between an ion and an electron, M 2 is very small compared with MI, this becomes
Mi
M. 1 M.'
Thus, if Q is the ionizing potential, the minimum value of T, which will communicate this energy to the electron, is - JTJ- Q.
- t 1V12
For the smallest possible ion, an atom of hydrogen, Mi/M 2 = 1,700, so that the minimum energy that will enable an ion to ionize a gas by knocking out an electron from a molecule is equal to 425Q. Q for many gases is about 10 volts; thus a positive ion must have at least energy represented by 4,250 volts to ionize the gas. With more mas- sive ions the energy required for ionization would be still greater.
An ion with a mass equal to that of a molecule of oxygen would not ionize unless its energy were greater than 136,000 volts. Thus if any ionization by ions takes place in discharge tubes it must be due to ions of the lighter elements hydrogen or helium.
If the ion came into collision with the ion of the atom instead of with one of its electrons, it could, since its mass is comparable with that of the ion, give up to this a large fraction of its energy, a very much larger fraction than it is able to give to an electron. Inasmuch as it requires less work to dissociate a molecule into neutral atoms than to dissociate it into positively and negatively electrified ions, the result of such a collision is more likely to be the production of neutral atoms than of electrified ions.
An ion is, however, a much more complex thing than the simple charge of electricity which has in the preceding considerations been taken to represent the forces it exerts; and it may be that some strongly electronegative ions have such a strong attraction for an electron that when they pass through the molecule of a more elec- tropositive element they are able to capture one of its electrons and carry it away with them. This type of ionization would differ from the ordinary type, inasmuch as in it the electron is never free; it produces negative ions, the other negative electrons.
It is evident from the preceding considerations that except in very intense fields it must be the electrons and not the ions which produce ionization by collision. Let us consider what are the chances of an electron acquiring sufficient energy in a uniform elec- tric field; if the electron moved freely under the electric force X for a distance / it would acquire Xe/ units of energy. The electron in its course through the gas will come into collision with other bodies; its path will be deflected, possibly reversed, and in moving against the electric field it may lose all the energy it had previously acquired. Thus a collision of this type will destroy any ionizing power given to the electron by the electric force before the collision.
Let X be the average distance passed over by an electron between two collisions; then the chance of an electron moving through a
distance / without a collision is * ; but if it moves through a distance / it will acquire energy =T = Xc/, hence the chance of an
T
electron acquiring energy equal or greater than T is t , and the chance that it should acquire energy between T and T+dT
is ( x )dT. If it possess this amount of energy the chance dT ^ J
e* that it makes one ion per centimetre of path is nir^(T/Q I ) ; hence
the chance that an electron should make one pair of ions per centi- metre of path is:
T
