thorium, the amount of Th X is far too small to be detected by its weight.
This method can be used generally to calculate the relative amounts of any successive products in radio-active equilibrium, provided the value of λ for each product is known. For example, it will be shown later that uranium is the parent of radium and is half transformed in about 6 × 10^8 years, while radium and radium D are half transformed in 1300 and 40 years respectively. The weight of radium present in one gram of uranium, when equilibrium is established, is thus 2 × 10^{-6} grams, and the weight of radium D is 7 × 10^{-8} grams. In a mineral containing a ton of uranium there should be about 1·8 grams of radium and ·063 grams of radium D. Some recent experiments described in section 262 show that these theoretical estimates are about twice too great.
259. Rayless Changes. The existence of well-marked
changes in radium, thorium, and actinium, which are not accompanied
by the expulsion of α or β particles, is of great interest
and importance.
Since the rayless changes are not accompanied by any appreciable ionization of the gas, their presence cannot be detected by direct means. The rate of change of the substance can, however, be determined indirectly, as we have seen, by measurement of the variation with time of the activity of the succeeding product. The law of change has been found to be the same as for the changes which give rise to α rays. The rayless changes are thus analogous, in some respects, to the monomolecular changes observed in chemistry, with the difference that the changes are in the atom itself, and are not due to the decomposition of a molecule into simpler molecules or into its constituent atoms.
It must be supposed that a rayless change is not of so violent a character as one which gives rise to the expulsion of α or β particles. The change may be accounted for either by supposing that there is a re-arrangement of the components of the atom, or that the atom breaks up without the expulsion of its parts with sufficient velocity to produce ionization by collision with the gas. The latter point of view, if correct, at once indicates the possibility that undetected changes of a similar character may be
