Page:Radio-activity.djvu/280

 sharp quantitative test. If the rate of production of emanation goes on at the same rate in the solid compound where very little escapes, as in the solution where probably all escapes, the emanation must be occluded in the compound, and consequently there must be a sudden release of this emanation on solution of the compound. On account of the very slow decay of the activity of the emanation of radium, the effects should be far more marked in that compound than in thorium. From the point of view developed in section 133, the exponential law of decay of the emanation expresses the result that N_{t} the number of particles remaining unchanged at the time t is given by N_{t}/N_{0} =  e^{-λt},  where N_{0} is the initial number of particles present. When a steady state is reached, the rate of production q_{0} of fresh emanation particles is exactly balanced by the rate of change of the particles N_{0} already present, i.e.

q_{0} = λN_{0},

N_{0} in this case represents the amount of emanation "occluded" in the compound. Substituting the value of λ found for the radium emanation in section 145,

N_{0}/q_{0} = 1/λ = 463,000.

The amount of emanation stored in a non-emanating radium compound should therefore be nearly 500,000 times the amount produced per second by the compound. This result was tested in the following way.

A weight of ·03 gr. of radium chloride of activity 1000 times that of uranium was placed in a Drechsel bottle and a sufficient amount of water drawn in to dissolve it. The released emanation was swept out by a current of air into a small gas holder and then into a testing cylinder. The initial saturation current was proportional to N_{0}. A rapid current of air was then passed through the radium solution for some time in order to remove any slight amount of emanation which had not been removed initially. The Drechsel bottle was