chapter IV., but for simplicity, the exponential law is assumed in the following calculations.
Consider two parallel plates placed as in Fig. 1, one of which is covered with a uniform layer of radio-active matter. If the distance d between the plates is small compared with the dimensions of the plates, the ionization near the centre of the plates will be sensibly uniform over any plane parallel to the plates and lying between them. If q be the rate of production of ions at any distance x and q_{0} that at the surface, then q = q_{0}e^{-λx}. The saturation current i per unit area is given by
i = [integral]_{0}^d q e´ dx, where e´ is the charge on an ion,
= q_{0}e´ [integral]_{0}^d e^{-λx} dx = (q_{0}e´/λ)(1 - e^{-λd});
hence, when λd is small, i.e. when the ionization between the plates is nearly constant,
i = q_{0}e´ d.
The current is thus proportional to the distance between the plates. When λd is large, the saturation current i_{0} is equal to q_{0}e´/λ, and is independent of further increase in the value of d. In such a case the radiation is completely absorbed in producing ions between the plates, and i/i_{0} = 1 - e^{-λd}.
For example, in the case of a thin layer of uranium oxide spread
over a large plate, the ionization is mostly produced by rays the
intensity of which is reduced to half value in passing through
4·3 mms. of air, i.e. the value of λ is 1·6. The following table is an
example of the variation of i with the distance between the plates.
Distance Saturation Current
2·5 mms. 32
5 " 55
7·5 " 72
10 " 85
12·5 " 96
15 " 100
Thus the increase of current for equal increments of distance between the plates decreases rapidly with the distance traversed by the radiation.
