to measure directly the energy of the α and β rays. A comparison of the energy radiated in the two forms of rays can, however, be made indirectly by two distinct methods.
If it be assumed that the same amount of energy is required to produce an ion by either the α or the β ray, and that the same proportion of the total energy is used up in producing ions, an approximate estimate can be made of the ratio of the energy radiated by the α and β rays by measuring the ratio of the total number of ions produced by them. If λ is the coefficient of absorption of the β rays in air, the rate of production of ions per unit volume at a distance x from the source is
where q₀ is the rate of ionization at the source.
The total number of ions produced by complete absorption of the rays is
Now λ is difficult to measure experimentally for air, but an approximate estimate can be made of its value from the known fact that the absorption of β rays is approximately proportional to the density of any given substance.
For β rays from uranium the value of λ for aluminium is about 14, and λ divided by the density is 5·4. Taking the density of air as ·0012, we find that for air
λ = ·0065.
The total number of ions produced in air is thus 154q₀ when the rays are completely absorbed.
Now from the above table the ionization due to the β rays is ·0074 of that produced by α rays, when the β rays passed through a distance of 5·7 cms. of air.
Thus we have approximately
Therefore about ⅙ of the total energy radiated into air by a thin layer of uranium is carried by the β rays or electrons. The ratio for thorium is about ¹⁄₂₂ and for radium about ¹⁄₁₄, assuming the rays to have about the same average value of λ.
This calculation takes into account only the energy which is radiated out into the surrounding gas; but on account of the ease with which the α rays are absorbed, even with a thin layer, the greater proportion of the radiation is absorbed by the radio-active substance itself. This is seen to be the case when it is recalled that the α radiation of thorium or radium is reduced to half value after passing through a thickness of