atomic number definition

These experimental observations enabled Rutherford and Soddy to formulate a theory of radioactive change. They suggested that the atoms of radioactive elements undergo spontaneous disintegration with "the emission of a- or /3-particles and the formation of atoms of a new element. Then the intensity of the radioactivity, which has been called the activity, is proportional to the number of atoms which disintegrate per unit time. The activity, A, measured by one of the methods discussed in Chapter 2, may then be replaced by the number of atoms N, and Eq. (10-1) may be writtenis the equation which represents the change with time of the number of atoms of a single decaying radioactive substance. Differentiation of both sides of Eq. (10-4) giveswhere N(t) has been abbreviated as N. According to Eq. (10-5), the decrease "per linit time in the number of atoms of a radioactive element because of disintegration is proportional to the number of atoms which have not yet disintegrated. The proportionality factor is the disintegration constant, which is characteristic of a particular radioactive species.Equation (10-5) is the fundamental equation of radioactive decay. With this equation, and with two assumptions, it was possible to account for the growth of activity in the thorium or uranium fractions from which the ThX or UX had been removed. The assumptions are (1) that there is a constant production of a new radioactive substance (say UX) by the radioactive element (uranium), and (2) that the new substance (UX) itself disintegrates according to the law of Eq. (10-5). Suppose t^at Q atoms of UX are produced per second by a given mass of uranium, and let N be the number of atoms of UX present at time t after the complete removal of the initial amount of UX. Then the net rate of increase of UX atoms in the uranium fraction isEquation (10-7) is the same as the recovery equation (10-2) so that the theory gives the correct result for the growth of activity in the uranium or thorium after the removal of the X body. Equation (10-7) also shows that the number of UX atoms in the mass of uranium approaches an equilibrium value for large values of t given by -the ratio