Now, in the experiment, the electrometer readily measured a current of 10-3 electrostatic units. Taking the charge on an ion as 3·4 × 10-10 electrostatic units, this corresponds to a production in the testing vessel of about 3 × 106 ions per sec., which would be produced by about 40 expelled α particles per second. Each radiating particle cannot expel less than one α particle and may expel more, but it is likely that the number expelled by an atom of the thorium emanation is not greatly different from that expelled by an atom of the radium emanation.
In [section 133] it has been shown that, according to the law of decay, λN particles change per second when N are present. Thus, to produce 40 α particles, λN cannot be greater than 40. Since for the thorium emanation λ is ¹⁄₈₇, it follows that N cannot be greater than 3500. The electrometer thus detected the presence of 3500 particles of the thorium emanation, and since in the static method the volume of the condensing spiral was about 15 c.c., this corresponded to a concentration of about 230 particles per c.c. An ordinary gas at atmospheric pressure and temperature probably contains about 3·6 × 1019 molecules per c.c. Thus the emanation would have been detected on the spiral if it had possessed a partial pressure of less than 10-17 of an atmosphere.
It is not surprising then that the condensation point of the thorium emanation is not sharply defined. It is rather a matter of remark that condensation should occur so readily with so sparse a distribution of emanation particles in the gas; for, in order that condensation may take place, it is probable that the particles must approach within one another’s sphere of influence.
Now in the case of the radium emanation, the rate of decay is about 5000 times slower than that of the thorium emanation, and consequently the actual number of particles that must be present to produce the same ionization per second in the two cases must be about 5000 times greater in the case of radium than in the case of thorium. This conclusion involves only the assumption that the same number of rays is produced by a particle of emanation in each case, and that the expelled particles produce in their passage through the gas the same number of ions. The number of particles present, in order to be detected by the electrometer, in this experiment, must therefore have been about 5000 × 3500, i.e. about 2 × 107. The difference of behaviour in the two cases is well explained by the view that, for equal electrical effects, the number of radium emanation particles must be far larger than the number of thorium emanation particles. The probability of the particles coming into each other’s sphere of influence will increase very rapidly as the concentration of the particles increases, and, in the case of the radium emanation, once the temperature of condensation is attained, all but a small proportion of the total number of particles present will condense in a very short time. In the case of the thorium emanation, however, the temperature might be far below that of condensation, and yet a considerable portion remain uncondensed for comparatively long intervals. On this view the experimental results obtained might reasonably be expected. A greater proportion of emanation condenses the longer the time allowed for condensation under the same conditions. The condensation occurs more rapidly in hydrogen than in oxygen, as the diffusion is greater in the former gas. For the same reason the condensation occurs faster the lower the pressure of the gas present. Finally, when the emanation is carried by a steady stream of gas, a smaller proportion condenses than in the other cases, because the concentration of emanation particles per unit volume of gas is less under these conditions.
It is possible that the condensation of the emanations may not occur in the gas itself but at the surface of the containing vessel. Accurate observations of the temperature of condensation have so far only been made in a copper spiral, but condensation certainly occurs in tubes of lead or glass at about the same temperature as in tubes of copper.
169. In experiments that were made by the static method with a very large quantity of radium emanation, a slight amount of escape of the condensed emanation was observed several degrees below the temperature at which most of the emanation was released. This is to be expected, since, under such conditions, the electrometer is able to detect a very minute proportion of the whole quantity of the emanation condensed.
Special experiments, with a large quantity of emanation, that were made with the spiral immersed in a bath of rapidly boiling nitric oxide, showed this effect very clearly. For example, the condensed emanation began to volatilize at -155° C. In 4 minutes the temperature had risen to -153·5°, and the amount volatilized was four times as great as at -155°. In the next 5-½ minutes the temperature had increased to -152·3° and practically the whole quantity, which was at least fifty times the amount at the temperature of -153·5°, had volatilized.
It thus seems probable that, if the temperature were kept steady at the point at which volatilization was first observed, and the released emanation removed at intervals, the whole of the emanation would in course of time be liberated at that temperature. Curie and Dewar and Ramsay have observed that the emanation condensed in a U tube, immersed in liquid air, slowly escapes if the pump is kept steadily working. These results point to the probability that the condensed emanation possesses a true vapour pressure, but great refinements in experimental methods would be necessary before such a conclusion could be definitely established.
The true temperature of condensation of the thorium emanation is probably about -120° C., and that of radium about -150° C. Thus there is no doubt that the two emanations are quite distinct from each other in this respect, and also with regard to their radio-activity, although they both possess the property of chemical inertness. These results on the temperatures of condensation do not allow us to make any comparison of the condensation points of the emanations with those of known gases, since the lowering of the condensation points of gases with diminution of pressure has not been studied at such extremely minute pressures.
170. It has been found[[264]] that the activity of the thorium emanation, when condensed in the spiral at the temperature of liquid air, decayed at the same rate as at ordinary temperatures. This is in accord with results of a similar kind obtained by P. Curie for the radium emanation (section 145), and shows that the value of the radio-active constant is unaffected by wide variations of temperature.