Atomic Nucleus and Its Structural Properties Revision Notes

In these revision notes for Atomic Nucleus and Its Structural Properties, we cover the following key points:

• What is atom?
• What are the historical events that led in the discovery of atom?
• What are the atomic models in a chronological way?
• What are the Bohr postulates?
• What is atomic nucleus? What are its components?
• What is a chemical element? How chemical elements are arranged?
• What are isotopes and isobars?
• What is the atomic mass (weight)?
• How to calculate the dimensions of atomic nuclei?
• What is the average density of nuclear material?

Atomic Nucleus and Its Structural Properties Revision Notes

Nowadays, everybody knows that matter is made up by microscopic particles called atoms. However, the atomic structure was discovered only about one century ago, despite people have been aware of particle nature of matter since antiquity.

In 1887, Thompson discovered the negatively charged electric particles as basic atomic components. These particles were given the name "electrons". The fact that electrons contains a negative charge and the entire atom is neutral implied the existence of a balancing positive charge at the same amount inside the atom.

In 1888, Becquerel realized that uranium radiates naturally, without the need for any external source of energy such as the sunlight. In this way, he unintentionally discovered the phenomenon of natural radioactivity. He then studied further and more in detail this phenomenon and reached the conclusion that it was not the X-radiation already known but another form of an unknown radiation.

According to the Thomson atomic model (1898), often referred to as the "plum-pudding" model, the atom is a sphere of uniformly distributed positive charge about one angstrom in diameter (1 angstrom = 0.1 nm = 10^-10 m). Electrons are embedded in a regular pattern, like raisins in a plum pudding or watermelon, to neutralize the positive charge.

The key discovery in this regard was made in 1911, with the experiment carried out by Rutherford. According to his model, an atom consists on a small positively charged nucleus at its centre, where most of atomic mass is concentrated. As for electrons, they revolve around the nucleus to preserve the atom's electric neutrality. However, this model could not explain the stability of atom in the sense that when electrons revolve around the nucleus, they lose energy and eventually collide with the nucleus.

The issue of atom's stability was resolved by Niels Bohr, who in 1913 proposed a new model, in which electrons move in determined circular orbits around the nucleus, similarly to the revolution of planets around the Sun. This prevents them from losing energy during such revolutions.

With his atomic model, Bohr proposed two courageous postulates:

1. The postulate of stationary states: An electron can revolve around the nucleus in certain fixed orbits of definite energy without emission of any radiant energy. Such orbits are called stationary orbits.
2. The postulate of frequencies. An electron can make a transition from a stationary state of higher energy E₂ to a state of lower energy E₁ and in doing so, it emits a single photon of frequency f.

A generalized version of the second postulate would be:

"An atom (electron) can emit or absorb radiation only during its transition from one stationary energetic level (orbit) into another."

Atomic nucleus is not the smallest thing in the universe; there are other particles inside it. These particles are protons and neutrons. Protons and neutrons are often referred to with a common name - nucleons (particles located inside the nucleus). The number of protons in a nucleus (otherwise known as atomic number) is denoted by Z while that of neutrons by N. Hence, the number of nucleons (atomic mass) A is

The number of protons (atomic number) Z indicates the type of element. There are 118 types of (chemical) elements known so far, where each of them has a different atomic number. All of them are arranged in a table of elements, known as the periodic table.

If the number of protons Z in two different atoms is equal but the number of neutrons differs, these atoms are known as isotopes. However, both atoms still represent the same chemical element despite having a different atomic mass.

On the other hand, if two different chemical elements have the same number of nucleons A, they are called isobars. They differ from each other much more than isotopes, as isobars represent different materials, despite the atomic mass is almost equal.

Another number that appear near each element (below its symbol) in the periodic table is the atomic mass or atomic weight number A. In general, it is not a whole number and shows a mean value of all isotopes of a given element based on the percentage of their existence.

The unit used to indicate the atomic mass is not kilogram but amu (atomic mass unit) or simply u instead. Thus, in scientific terms, 1 u represents 1/12 of the mass of a C-12 nucleus and it is a rough value to indicate the mass of one proton or one neutron. The conversion factor between amu and kilogram is

The nucleus of an atom has very small dimensions, much smaller compared to those of the atom itself. Experiments show that if the nucleus is thought as a sphere, its radius ranges from 10_-14 m to 10^-15 m. The empirical formula

where r₀ is a constant (r₀ = 1.2 × 10^-15 m), is often used to calculate the radius r of nucleus for any element, and A is the number of nucleons contained in the nucleus of the given element. Thus, the formula that calculates the radius of atomic nuclei is

Despite the volume of atomic nucleus is much smaller compared to the volume of the atom itself, the mass of atom is almost entirely concentrated in the nucleus (only electrons that are much lighter than protons and neutrons are outside the nucleus). Therefore, the density of atomic nuclei is much greater than the density of the corresponding atoms.