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
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[[332]]. 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.