2.1 Atomic Nuclei

2.1.1 Components of Nuclei

The atomic nuclei were discovered by the English physicist Ernest Rutherford on the basis of Ernest Mardsen’s experiments (Figure 2.1). In their experiments, Mardsen and Hans Geiger studied the backscattering of alpha rays (which were known to be positively charged) from a gold plate and observed that a very small portion of these particles (about 1 in 100,000) were scattered back at an angle of 180°. Since the backscattering of the positive alpha particles is directed by electrostatic forces, this is possible only if a very high portion of the positive charge of the atom is concentrated in very little volume. This small component of the atom is the atomic nucleus. The backscattered portion of the alpha parti­cles indicates that the radius of the nucleus is about 105 times smaller than the radius of the atom.

In addition to the positive charge, the mass of the atom is concentrated in the nucleus. The radius of the atomic nuclei (R) can be expressed approximately by Eq. (2.1):

R = R0 X A1/3 (2.1)

where A is the mass number and R0 is the radius of the nucleus of the hydrogen atom (~ 1.3 X 10_15 m). As a consequence of Eq. (2.1), the density of any atomic nucleus is approximately the same (p = 2 X 1017 kg/m3), independent of the iden­tity of the atoms. The mass of the nucleus is evenly distributed in the nucleus. This density then decreases quite abruptly to reach the density of the electron shell (which is very small—practically zero) at a distance of about 2.5 X 1015 m from the nucleus. Similarly, the charge density surrounding the nucleus decreases over the same distance to reach the charge density of the electron shell, which is comparatively very small due to the relatively large size of the electron shell (about 10_1° m).

The alpha backscattering experiments proved that the atomic nuclei have mass, charge, and well-defined geometric size. At the time of the alpha backscattering experiments, not much was known about neutrons. It was conceptualized that in order to neutralize the positive charge of the protons, electrons must be present in the nucleus. This model is called J. J. Thomson’s atomic model. According to this model, atomic

Nuclear and Radiochemistry. DOI: http://dx. doi. org/10.1016/B978-0-12-391430-9.00002-0

© 2012 Elsevier Inc. All rights reserved.

nuclei should comprise protons and electrons. This model, however, can be disproved easily by the zero-point energy of the electron in the nucleus. Heisenberg’s uncertainty principle says that

where Дх and Дv are the uncertainty of the determination of the position and velocity, respectively; h is Planck’s constant; and m is the mass of the particle. The radius of the nucleus (R) can be substituted for Дх in the equation; if Дх > R, then the electron is outside the nucleus. From Eq. (2.2), Дv, and from here the energy of the electron, can be expressed as follows:

These calculations for the nucleus show that the zero-point energy of the electron is two orders of magnitude greater than the binding energy of nucleons (7—8 MeV/nucleon). Thus, if the electrons were restricted in the nucleus, their energy would be so high that they would leave it instantly. So, it is clearly proved that electrons cannot be present in the nucleus. Subsequently, in 1920, Rutherford conceptualized that the nucleus contains neutral particles that explain the difference between the charge and the mass of the nucleus. These particles were called “neutrons,” and they were experimentally demonstrated by James Chadwick in 1932 (Section 5.5.1).

Atomic nuclei consist of protons and neutrons. The number of protons is the atomic number (Z), and the sum of the number of protons (Z) and neutrons (N) is the mass number (A). The particles composing the nuclei are called “nucleons.”