A, B and C are too small to weigh. It may be possible, however, to detect their presence by means of the spectroscope.
In the case of thorium, the weight of the product Th X, which is present in greatest quantity, is far too small to be detected. Since the value of λ for Th X is about the same as for the radium emanation, the maximum weight present per gram is about 4 × 10-12 of a gram, remembering that q for radium is about 2 × 106 times the value for thorium. Even with a kilogram of 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 × 108 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