a + b = 0;
hence b = -a = N₀,
and the equation becomes
This is equivalent to the equation already obtained in [section 130], since the intensity of the radiation is always proportional to the number of particles present.
134. Influence of conditions on the rate of decay. Since the activity of any product, at any time, may be taken as a measure of the rate at which chemical change takes place, it may be used as a means of determining the effect of conditions on the changes occurring in radio-active matter. If the rate of change should be accelerated or retarded, it is to be expected that the value of the radio-active constant λ will be increased or decreased, i.e. that the decay curve will be different under different conditions.
No such effect, however, has yet been observed in any case of radio-active change, where none of the active products produced are allowed to escape from the system. The rate of decay is unaltered by any chemical or physical agency, and in this respect the changes in radio-active matter are sharply distinguished from ordinary chemical changes. For example, the rate of decay of activity from any product takes place at the same rate when the substance is exposed to light as when it is kept in the dark, and at the same rate in a vacuum as in air or any other gas at atmospheric pressure. Its rate of decay is unaltered by surrounding the active matter by a thick layer of lead under conditions where no ordinary radiation from outside can affect it. The activity of the matter is unaffected by ignition or chemical treatment. The material giving rise to the activity can be dissolved in acid and re-obtained by evaporation of the solution without altering the activity. The rate of decay is the same whether the active matter is retained in the solid state or kept in solution. When a product has lost its activity, resolution or heat does not regenerate it, and as we shall see later, the rate of decay of the active products, so far examined, is the same at a red heat as at the temperature of liquid air. In fact, no variation of physical or chemical conditions has led to any observable difference in the decay of activity of any of the numerous types of active matter which have been examined.
135. Effect of conditions on the rate of recovery of activity. The recovery of the activity of a radio-element with time, when an active product is separated from it, is governed by the rate of production of fresh active matter and by the decay of activity of that already produced. Since the rate of decay of the activity of the separated product is independent of conditions, the rate of recovery of activity can be modified only by a change of the rate of production of fresh active matter. As far as experiments have gone, the rate of production, like the rate of decay, is independent of chemical or physical conditions. There are indeed certain cases which are apparent exceptions to this rule. For example, the escape of the radio-active emanations from thorium and radium is readily affected by heat, moisture and solution. A more thorough investigation, however, shows that the exception is only apparent and not real. These cases will be discussed more in detail in [chapter VII], but it may be stated here that the differences observed are due to differences in the rate of escape of the emanations into the surrounding gas, and not to differences in the rate of production. For this reason it is difficult to test the question at issue in the case of the thorium compounds, which in most cases readily allow the emanation produced by them to escape into the air.
In order to show that the rate of production is independent of molecular state, temperature, etc., it is necessary in such a case to undertake a long series of measurements extending over the whole time of recovery. It is impossible to make accurate relative comparisons to see if the activity is altered by the conversion of one compound into another. The relative activity in such a case, when measured by spreading a definite weight of material uniformly on a metal plate, varies greatly with the physical conditions of the precipitate, although the total activity of two compounds may be the same.
The following method[[230]] offers an accurate and simple means of studying whether the rate of production of active matter is influenced by molecular state. The substance is chemically converted into any compound required, care being taken that active products are recovered during the process. The new compound is then spread on a metal plate and compared with a standard sample of uranium for several days or weeks as required. If the rate of production of active matter is altered by the conversion, there should be an increase or decrease of activity to a new steady value, where the production of active matter is again balanced by the rate of decay. This method has the great advantage of being independent of the physical condition of the precipitate. It can be applied satisfactorily to a compound of thorium like the nitrate and the oxide which has been heated to a white heat, after which treatment only a slight amount of emanation escapes. The nitrate was converted into the oxide in a platinum crucible by treatment with sulphuric acid and ignition to a white heat. The oxide so obtained was spread on a plate, but no change of its activity was observed with time, showing that in this case the rate of production was independent of molecular state. This method, which is limited in the case of thorium, may be applied generally to the uranium compounds where the results are not complicated by the presence of an emanation.