Ionization Currents Produced by Radon, RaA and RaC′ in Cylindrical Ionization Chambers

A general theoretical equation is derived for the ionization produced in cylindrical ionization chambers by Rn and its decay products. Where $\frac{\mathrm{dv}}{\mathrm{dt}}\equiv$ volts per sec. discharge, $j\equiv$ fractional saturation of the ion current, $C\equiv$ electrostatic capacity in cm, $A\equiv$ curies of Rn present at time $t=0\mathrm{}$, ${\lambda }_1\equiv$ decay constant of Rn, $\frac{1}{\mu }\equiv$ stopping power of the gas in the ionization chamber, $d\equiv$ cm diameter and $h\equiv$ cm height of the chamber, and $t\ge 3$ hr.: $\frac{\mathrm{dv}}{\mathrm{dt}}=5.3\mathrm{}\times {10}^8\left(\frac{j}{C}\right)(3.57-5.00\mathrm{}\frac{\mu }{h}-3.47\mathrm{}\frac{\mu }{d}+5.48\mathrm{}\frac{{\mu }^2}{\mathrm{hd}})A{e}^{-{\lambda }_{1}t}$ when $d$ and $h$ are greater than twice 6.60μ cm, the range of the RaC′ alpha-ray. Experimental confirmation employing standard radium solutions is described. Where either $C$ or $A$ is known, the other may be computed, therefore Rn ionization may be employed for absolute capacity measurements. General equations are also derived for alpha-ray ionization (1) above a plane surface due to a homogeneous radioactive substance below the plane, and (2) a radioactive substance uniformly distributed on a wire normal to the plane, and (3) for the ionization outside a dihedral right angle enclosing a homogeneous radioactive substance.