as 225, the number of atoms in 1 gram of radium is equal to 3·6 × 10^{21}. The fraction λ of radium which breaks up is thus 1·95 × 10^{-11} per second, or 5·4 × 10^{-4} per year. It follows that in each gram of radium about half a milligram breaks up per year. The average life of radium is about 1800 years, and half of the radium is transformed in about 1300 years.
We shall now consider the calculation, based on the observed result of Ramsay and Soddy, that the volume of emanation to be obtained from one gram of radium is about 1 cubic millimetre. The experimental evidence based on diffusion results indicates that the molecular weight of the emanation is about 100. If the disintegration theory is correct, the emanation is an atom of radium minus one particle, and therefore must have a molecular weight of at least 200. This high value is more likely to be correct than the experimental number, which is based on evidence that must necessarily be somewhat uncertain. Now the rate of production of emanation per second is equal to λN_{0}, where N_{0} is the equilibrium amount. Taking the molecular weight as 200, the weight of emanation produced per second from 1 gram of radium = 8·96 × 10^{-6}λ = 1·9 × 10^{-11} gram.
Now the weight of emanation produced per second is very nearly equal to the weight of radium breaking up per second. Thus the fraction of radium breaking up per second is about 1·9 × 10^{-11}, which is in agreement with the number previously calculated by the first method.
We may thus conclude that radium is half transformed in about 1300 years.
Taking the activity of pure radium as about two million times that of uranium, and remembering that only one change, which gives rise to α rays, occurs in uranium and four in radium, it can readily be calculated that the fraction of uranium changing per year is about 10^{-9}. From this it follows that uranium should be half transformed in about 6 × 10^8 years.
If thorium is a true radio-active element, the time for half transformation is about 2·4 × 10^9 years, since thorium has about the same activity as uranium but contains four products which emit α rays. If the activity of thorium is due to some radio-active impurity, no estimate of the length of its life can be made until
