101. Connection between absorption and density. Since in all cases the radiations first diminish approximately according to an exponential law with the distance traversed, the intensity I after passing through a thickness x is given by I = I_{0}e^{-λx} where λ is the absorption constant and I_{0} the initial intensity.
The following table shows the value of λ with different radiations for air and aluminium.
Radiation λ for aluminium λ for air
Excited radiation 830 ·42
Thorium 1250 ·69
Radium 1600 ·90
Uranium 2750 1·6
Taking the density of air at 20° C. and 760 mms. as 0·00120 compared with water as unity, the following table shows the value of λ divided by density for the different radiations.
Radiation Aluminium Air
Excited radiation 320 350
Thorium 480 550
Radium 620 740
Uranium 1060 1300
Comparing aluminium and air, the absorption is thus roughly proportional to the density for all the radiations. The divergence, however, between the absorption-density numbers is large when two metals like tin and aluminium are compared. The value of λ for tin is not much greater than for aluminium, although the density is nearly three times as great.
If the absorption is proportional to the density, the absorption in a gas should vary directly as the pressure, and this is found to be the case. Some results on this subject have been given by the writer (loc. cit.) for uranium rays between pressures of 1/4 and 1 atmosphere. Owens (loc. cit.) examined the absorption of the α radiation in air from thoria between the pressures of 0·5 to 3 atmospheres and found that the absorption varied directly as the pressure.
The variation of absorption with density for the projected positive particles is thus very similar to the law for the projected negative particles and for cathode rays. The absorption, in both cases, depends mainly on the density, but is not in all cases directly
