The value of α, which may be termed the _coefficient of recombination_,
has been determined in absolute measure by Townsend[52], McClung[53] and
Langevin[54] by different experimental methods but with very concordant
results. Suppose, for example, with the apparatus of Fig. 6, the time
_T_, taken for half the ions to recombine after passing by the electrode
_A_, has been determined experimentally. Then
1
--- = α_T_,
_N_
where _N_ is the number of ions per c.c. present at _A_. If the
saturation current _i_ is determined at the electrode _A_, _i = NVe_,
where _e_ is the charge on an ion and _V_ is the volume of uniformly
ionized gas carried by the electrode _A_ per second. Then
_Ve_
α = ----- .
_iT_
The following table shows the value of α obtained for different gases.
_Value of_ α.
Gas Townsend McClung Langevin
Air 3420 × _e_ 3384 × _e_ 3200 × _e_
Carbon 3500 × _e_ 3492 × _e_ 3400 × _e_
Dioxide
Hydrogen 3020 × _e_
The latest determination of the value of _e_ (see section 36) is 3·4 ×
10⁻¹⁰ E.S. units; thus α = 1·1 × 10⁻⁶.
Using this value, it can readily be shown from the equation of
recombination that, if 10⁶ ions are present per c.c., half of them
recombine in about 0·9 sec. and 99% in 90 secs.
McClung (_loc. cit._) showed that the value of α was approximately
independent of the pressure between ·125 and three atmospheres. In later
observations, Langevin has found that the value of α decreases rapidly
when the pressure is lowered below the limits used by McClung.
=31.= In experiments on recombination it is essential that the gas
should be free from dust or other suspended particles. In dusty air, the
rate of recombination is much more rapid than in dust-free air, as the
ions diffuse rapidly to the comparatively large dust particles
distributed throughout the gas. The effect of the suspension of small
particles in a conducting gas is very well illustrated by an experiment
of Owens[55]. If tobacco smoke is blown between two parallel plates as
in Fig. 1, the current at once diminishes to a small fraction of its
former value, although a P.D. is applied sufficient to produce
saturation under ordinary conditions. A much larger voltage is then
necessary to produce saturation. If the smoke particles are removed by a
stream of air, the current returns at once to its original value.
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