Page:Radio-activity.djvu/193

 All the particles coming from a depth x of the material given by h = a - [Greek: rho]x will enter the ionization vessel. The number of ions produced in a depth dh of the ionization vessel is equal to nxdh, i.e. to n((a - h)/[Greek: rho])dh, where n is a constant.

If the depth of the ionization vessel be b, the total number of ions produced in the vessel is

[integral]_{h}^{h + b} (n((a - h)/[Greek: rho])dh) = (nb/[Greek: rho])(a - h - b/2).

This supposes that the stream of particles passes completely across the vessel. If not, the expression becomes

[integral]_{h}^a (n((a - h)/[Greek: rho])dh) = n(a - h)^2/(2[Greek: rho]).

If the ionization in the vessel AB is measured, and a curve plotted showing its relation to h, the curve in the former case should be a straight line whose slope is nb/[Greek: rho] and in the latter a parabola.

Thus if a thin layer of radio-active material is employed and a shallow ionization vessel, the ionization would be represented by a curve such as APM (Fig. 40), where the ordinates represent distances from the source of radiation, and the abscissae the ionization current between the plates AB.

Fig. 40.

In this case, PM is the range of the [Greek: alpha] particles from the lowest layer of the radio-active matter. The current should be constant for all distances less than PM.

For a thick layer of radio-active matter, the curve should be a straight line such as APB.

Curves of the above character should only be obtained when definite cones of rays are employed, and where the ionization vessel is shallow and includes the whole cone of rays. In such a case the inverse square law need not be taken into account.