If each atom of the product expels one α particle, the total energy emitted from 1 gram of the matter is about 2 × 1016 ergs or 8 × 108 gram calories. The total emission of energy from a product which emits only β rays is probably about one-hundredth of the above amount.
In this case we have only considered the energy emitted from a single product independently of the successive products which may arise from it. Radium, for example, may be considered a radio-active product which slowly breaks up and gives rise to four subsequent α ray products. The total heat emission from one gram of radium and products is thus about five times the above amount, or 4 × 109 gram calories.
The total emission of energy from radium is discussed later in [section 266] from a slightly different point of view.
252. Number of ions produced by an α particle. In the first edition of this book it was calculated by several independent methods that 1 gram of radium emitted about 1011 α particles per second. Since the actual number has later been determined by measuring the charge carried by the α rays ([section 93]) we can, conversely, use this number to determine with more certainty some of the constants whose values were assumed in the original calculation.
For example, the total number of ions produced by an α particle in the gas can readily be determined. The method employed is as follows. 0·484 mgr. of radium bromide was dissolved in water and then spread uniformly over an aluminium plate. After evaporation, the saturation ionization current, due to the radium at its minimum activity, was found to be 8·4 × 10-8 ampere. The plates of the testing vessel were sufficiently far apart to absorb all the α rays in the gas. The number of α particles expelled per second into the gas was found experimentally to be 8·7 × 106. Taking the charge on an ion as 1·13 × 10-19 coulombs ([section 36]), the total number of ions produced per second in the gas was 7·5 × 1011. Thus each α particle on an average produced 86,000 ions in the gas before it was absorbed.
Now Bragg ([section 104]) has shown that the α particles from radium at its minimum activity are stopped in about 3 cms. of air. The results obtained by him indicate that the ionization of the particles per cm. of path is less near the radium than some distance away. Assuming, however, as a first approximation that the ionization is uniform along the path, the number of ions produced per cm. of path by the α particle is 29,000. Since the ionization varies directly as the pressure, at a pressure of 1 mm. of mercury the number of ions per unit path would be about 38. Now Townsend ([section 103]) found that the maximum number of ions produced per unit path of air at 1 mm. pressure by an electron in motion was 20, and in this case a fresh pair of ions was produced at each encounter of the electron with the molecules in its path. In the present case the α particle, which has a very large mass compared with the electron, appears to have a larger sphere of influence than the electron and to ionize twice as many molecules.
In addition, the α particle produces many more ions per unit path than an electron moving with the same velocity, for it has been shown ([section 103]) that the electron becomes a less efficient ionizer after a certain velocity is reached. As Bragg (loc. cit.) has pointed out, this is to be expected, since the α particle consists of a large number of electrons and consequently would be a far more efficient ionizer than an isolated electron. A calculation of the energy required to produce an ion by an α particle is given in [Appendix A].
253. Number of β particles expelled from one gram of radium. It is of importance to compare the total number of β particles expelled from one gram of radium in radio-active equilibrium, as, theoretically, this number should bear a definite relation to the total number of α particles emitted. We have seen that new radium in radio-active equilibrium contains four products which emit α rays, viz. radium itself, the emanation, radium A and radium C. On the other hand, β rays are expelled from only one product, radium C. The same number of atoms of each of these successive products in equilibrium break up per second. If the disintegration of each atom is accompanied by the expulsion of one α particle and, in the case of radium C, also of one β particle, the number of α particles emitted from radium in radio-active equilibrium will be four times the number of β particles.
The method employed by Wien to determine the number of β particles emitted from a known quantity of radium has already been discussed in [section 80]. On account of the absorption of some of the β particles in the radium envelope and in the radium itself, the number found by him is far too small. It has been shown in [section 85] that a number of easily absorbed β rays are projected from radium, many of which would be stopped in the radium itself or in the envelope containing it.
In order to eliminate as far as possible the error due to this absorption, in some experiments made by the writer, the active deposit obtained from the radium emanation rather than radium itself was used as a source of β rays. A lead rod, 4 cms. long and 4 mms. in diameter, was exposed as the negative electrode in a large quantity of the radium emanation for three hours. The rod was then removed and the γ ray effect from it immediately measured by an electroscope and compared with the corresponding γ ray effect from a known weight of radium bromide in radio-active equilibrium. Since the active deposit contains the product radium C which alone emits β rays, and, since the intensities of the β and γ rays are always proportional to each other, the number of β particles expelled from the lead rod per second is equal to the corresponding number from the weight of radium bromide which gives the same γ ray effect as the lead rod.