Page:Radio-activity.djvu/497

 time t by qe^{-λt}, where λ is the constant of decay of activity of radium and of the initial heating effect; the total heat emission from 1 gram of radium is given by [integral]_{0}^[infinity] qe^{-λt} dt = q/λ.

Now on the estimate of the life of radium given in section 261 the value of λ is 1/1850 when 1 year is taken as the unit of time. The total heat emission from 1 gram of radium during its life is thus 1·6 × 10^9 gram-calories. The heat emitted in the union of hydrogen and oxygen to form 1 gram of water is about 4 × 10^3 gram-calories, and in this reaction more heat is given out for equal weights than in any other chemical reaction known. It is thus seen that the total energy emitted from 1 gram of radium during its changes is about one million times greater than in any known molecular change. That matter is able, under special conditions, to emit an enormous amount of energy, is well exemplified by the case of the radium emanation. Calculations of the amount of this energy have already been given in section 249.

Since the other radio-elements only differ from radium in the slowness of their change, the total heat emission from uranium and thorium must be of a similar high order of magnitude. There is thus reason to believe that there is an enormous store of latent energy resident in the atoms of the radio-elements. This store of energy could not have been recognized if the atoms had not been undergoing a slow process of disintegration. The energy emitted in radio-active changes is derived from the internal energy of the atoms. The emission of this energy does not disobey the law of the conservation of energy, for it is only necessary to suppose that, when the radio-active changes have ceased, the energy stored up in the atoms of the final products is less than that of the original atoms of the radio-elements. The difference between the energy originally possessed by the matter which has undergone the change, and the final inactive products which arise, is a measure of the total amount of energy released.

There seems to be every reason to suppose that the atomic energy of all the elements is of a similar high order of magnitude. With the exception of their high atomic weights, the radio-elements do not possess any special chemical characteristics which differentiate them from the inactive elements. The existence of