An approximate estimate of the rate of change of radium can easily be made by two different methods depending upon (1) the number of atoms of radium breaking up per second, and (2) the amount of emanation produced per second.
It has been shown experimentally ([section 93]) that 1 gram of radium at its minimum activity expels 6·2 × 1010 α particles per second. The heating effect of radium and also its volume agree closely with calculation, if it is supposed that each atom of each product in breaking up emits one α particle. On this supposition it is seen that 6·2 × 1010 atoms of radium break up per second.
Now it has been shown experimentally (section 39) that one cubic centimetre of hydrogen at standard pressure and temperature contains 3·6 × 1019 molecules. Taking the atomic weight of radium as 225, the number of atoms in 1 gram of radium is equal to 3·6 × 1021. 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 λN₀, where N₀ is the equilibrium amount. Taking the molecular weight as 200, the weight of emanation produced per second from 1 gram of radium = 8·96 × 10-6λ = 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 × 108 years.
If thorium is a true radio-active element, the time for half transformation is about 2·4 × 109 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 the primary active substance has been isolated and its activity measured.
262. Origin of radium. The changes in radium are thus fairly rapid, and a mass of radium if left to itself should in the course of a few thousand years have lost a large proportion of its radio-activity. Taking the above estimate of the life of radium, the value of λ is 5·4 × 10-4, with a year as the unit of time. A mass of radium left to itself should be half transformed in 1300 years and only one-millionth part would remain after 26,000 years. Thus supposing, for illustration, that the earth was originally composed of pure radium, its activity per gram 26,000 years later would not be greater than the activity observed to-day in a good specimen of pitchblende. Even supposing this estimate of the life of radium is too small, the time required for the radium practically to disappear is short compared with the probable age of the earth. We are thus forced to the conclusion that radium is being continuously produced in the earth, unless the very improbable assumption is made, that radium was in some way suddenly formed at a date recent in comparison with the age of the earth. It was early suggested by Rutherford and Soddy[[351]] that radium might be a disintegration product of one of the radio-elements found in pitchblende. Both uranium and thorium fulfil the conditions required in a possible source of production of radium. Both are present in pitchblende, have atomic weights greater than that of radium, and have rates of change which are slow compared with that of radium. In some respects, uranium fulfils the conditions required better than thorium; for it has not been observed that minerals rich in thorium contain much radium, while on the other hand, the pitchblendes containing the most radium contain a large proportion of uranium.
If radium is not produced from uranium, it is certainly a remarkable coincidence that the greatest activity of pitchblende yet observed is about five or six times that of uranium. Since radium has a life short compared with that of uranium, the amount of radium produced should reach a maximum value after a few thousand years, when the rate of production of fresh radium—which is also a measure of the rate of change of uranium—balances the rate of change of that product. In this respect the process would be exactly analogous to the production of the emanation by radium, with the difference that the radium changes much more slowly than the emanation. But since radium itself in its disintegration gives rise to at least five changes with the corresponding production of α rays, the activity due to the radium (measured by the α rays), when in a state of radio-active equilibrium with uranium, should be about five times that of the uranium that produces it; for it has been shown that only one change has so far been observed in uranium in which α rays are expelled. Taking into account the presence of actinium in pitchblende, the activity observed in the best pitchblende is about the same as would be expected if the radium were a disintegration product of uranium. If this hypothesis is correct, the amount of radium in any pitchblende should be proportional to the amount of uranium present, provided the radium is not removed from the mineral by percolating water.