Section 114 That the Kinetic Energy of the β Particles Emitted From

radium is probably not greater than one per cent. of that due to the α particles. If the heat emission is a result of bombardment by the particles expelled from its mass, it is to be expected that the heating effect of the β rays will be very small compared with that due to the α rays. This anticipation is borne out by experiment. Curie measured the heating effect of radium (1) when enclosed in a thin envelope, and (2) when surrounded by one millimetre of lead. In the former case a large proportion of the β rays escaped, and, in the latter, nearly all were absorbed. The increase of heating effect in case (2) was not more than five per cent., and this is probably an over-estimate.

In a similar way, since the total ionization due to the β rays is about equal to that produced by the γ rays, we should expect that the heating effect of the γ rays will be very small compared with that arising from the α rays.

Paschen made some experiments on the heating effect of radium in a Bunsen ice calorimeter where the radium was surrounded by a thickness of 1·92 cms. of lead—a depth sufficient to absorb a large proportion of the γ rays. In his first publication, results were given which indicated that the heating effect of the γ rays was even greater than that of the α rays. This was not confirmed by later observations by the same method. He concluded that the ice calorimeter could not be relied on to measure such very small quantities of heat.

After the publication of Paschen’s first paper Rutherford and Barnes examined the question by a different method. An air calorimeter of the form shown in Fig. 98 was employed which was found to give very satisfactory results. The heat emission of radium was measured (1) when the radium was surrounded by a cylinder of aluminium and (2) when surrounded by a cylinder of lead of the same dimensions. The aluminium absorbed only a small fraction of the γ rays while the lead stopped more than half. No certain difference between the heating effect in the two cases was observed, although from the earlier experiments of Paschen a difference of at least 50 per cent. was to be expected.

We must therefore conclude that the β and γ rays together do not supply more than a small percentage of the total heat emission of radium—a result which is in accordance with the calculations based on the total ionization produced by the different types of rays.

=248. Source of the energy.= It has been shown that the heating effect of radium is closely proportional to the activity measured by the α rays. Since the activity is generally measured between parallel plates such a distance apart that most of the α particles are absorbed in the gas, this result shows that the heating effect is proportional to the energy of the emitted α particles. The rapid heat emission of radium follows naturally from the disintegration theory of radio-activity. The heat is supposed to be derived not from external sources, but from the internal energy of the radium atom. The atom is supposed to be a complex system consisting of charged parts in very rapid motion, and in consequence contains a large store of latent energy, which can only be manifested when the atom breaks up. For some reason, the atomic system becomes unstable, and an α particle, of mass about twice that of the hydrogen atom, escapes, carrying with it its energy of motion. Since the α particles would be practically absorbed in a thickness of radium of less than ·001 cm., the greater proportion of the α particles, expelled from a mass of radium, would be stopped in the radium itself and their energy of motion would be manifested in the form of heat. The radium would thus be heated by its own bombardment above the temperature of the surrounding air. The energy of the expelled α particles probably does not account for the whole emission of heat by radium. It is evident that the violent expulsion of a part of the atom must result in intense electrical disturbances in the atom. At the same time, the residual parts of the disintegrated atom rearrange themselves to form a permanently or temporarily stable system. During this process also some energy is probably emitted, which is manifested in the form of heat in the radium itself.

The view that the heat emission of radium is due very largely to the kinetic energy possessed by the expelled α particles is strongly confirmed by calculations of the magnitude of the heating effect to be expected on such an hypothesis. It has been shown in section 93 that one gram of radium bromide emits about 1·44 × 10¹¹ α particles per second. The corresponding number for 1 gram of radium (Ra = 225) is 2·5 × 10¹¹. Now it has been calculated from experimental data in section 94, that the average kinetic energy of the α particles expelled from radium is 5·9 × 10⁻⁶ ergs. Since all of the α particles are absorbed either in the radium itself or the envelope surrounding it, the total energy of the α particles emitted per second is 1·5 × 10⁶ ergs. This corresponds to an emission of energy of about 130 gram calories per hour. Now the observed heating effect of radium is about 100 gram calories per hour. Considering the nature of the calculation, the agreement between the observed and experimental values is as close as would be expected, and directly supports the view that the heat emission of radium is due very largely to the bombardment of the radium and containing vessel by the α particles expelled from its mass.

=249. Heating effect of the radium emanation.= The enormous amount of heat liberated in radio-active transformations which are accompanied by the expulsion of α particles is very well illustrated by the case of the radium emanation.

The heat emission of the emanation released from 1 gram of radium is 75 gram calories per hour at its maximum value. This heat emission is not due to the emanation alone, but also to its further products which are included with it. Since the rate of heat emission decays exponentially with the time to about half value in four days, the total amount of heat liberated during the life of the emanation from 1 gram of radium is equal to

$$ \int₀^{\infty} 75 e^{–λt} dt = \frac {75} {λ} $$

= 10,000 gram calories approximately,

since λ = ·0072(hour)⁻¹. Now the volume of the emanation from 1 gram of radium is about 1 cubic millimetre at standard pressure and temperature (section 172). Thus 1 cubic centimetre of the emanation would during its transformation emit 10⁷ gram calories. The heat emitted during the combination of 1 c.c. of hydrogen and oxygen to form water is about 2 gram calories. The emanation thus gives out during its changes 5 × 10⁶ times as much energy as the combination of an equal volume of hydrogen and oxygen to form water, although this latter reaction is accompanied by a larger release of energy than any other known to chemistry.

The production of heat from 1 c.c. of the radium emanation is about 21 gram calories per second. This generation of heat would be sufficient to heat to redness, if not to melt down, the walls of the glass tube containing the emanation.

The probable rate of heat emission from 1 gram weight of the emanation can readily be deduced, assuming that the emanation has about 100 times the molecular weight of hydrogen. Since 100 c.c. of the emanation would weigh about 1 gram, the total heat emission from 1 gram of the emanation is about 10⁹ gram calories.

It can readily be calculated that one pound weight of the emanation would, at its maximum, radiate energy at the rate of about 10,000 horse-power. This radiation of energy would fall off with the time, but the total emission of energy during the life of the emanation would correspond to 60,000 horse-power days.

=250. Heating effects of uranium, thorium, and actinium.= Since the heat emission of radium is a direct consequence of its bombardment by the α particles expelled from its mass, it is to be expected that all the radio-elements which emit α rays should also emit heat at a rate proportional to their α ray activity.

Since the activity of pure radium is probably about two million times that of uranium or thorium, the heat emission from 1 gram of thorium or uranium should be about 5 × 10⁻⁵ gram calories per hour, or about 0·44 gram calories per year. This is a very small rate of generation of heat, but it should be detectable if a large quantity of uranium or thorium is employed. Experiments to determine the heating effect of thorium have been made by Pegram. Three kilograms of thorium oxide, enclosed in a Dewar bulb, were kept in an ice-bath, and the difference of temperature between the thorium and ice-bath determined by a set of iron-constantan thermo-electric couples. The maximum difference of temperature observed was 0·04° C., and, from the rate of change of temperature, it was calculated that one gram of thorium oxide liberated 8 × 10⁻⁵ gram calories per hour. A more accurate determination of the heat emission is in progress, but the results obtained are of the order of magnitude to be expected.

=251. Energy emitted by a radio-active product.= An important consequence follows from the fact that the heat emission is a measure of the energy of the expelled α particles. If each atom of each product emits α particles, the total emission of energy from 1 gram of the product can at once be determined. The α particles from the different products are projected with about the same velocity, and consequently carry off about the same amount of energy. Now it has been shown that the energy of each α particle expelled from radium is about 5·9 × 10⁻⁶ ergs. Most of the products probably have an atomic weight in the neighbourhood of 200. Since there are 3·6 × 10¹⁹ molecules in one cubic centimetre of hydrogen, it can easily be calculated that there are about 3·6 × 10²¹ atoms in one gram of the product.

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