# The Notion of Mass Number

The concept of the mass number is directly related to such concepts as atom, the structure of the atomic nucleus, atomic number, protons, electrons, neutrons, as well as nuclear power. Below, let’s successively study each of these concepts.

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• Atom

All matter is composed of tiny building blocks called atoms. These atoms can’t be separated by any chemical methods, however, they are able to connect with each other forming substance. Separate atoms are very small (approximately 10-10 meters in diameter) and they can’t be directly observed with any measuring instruments. Despite their small size, atoms themselves are composed of a number of other particles – protons, electrons, and neutrons. Since the masses of these particles are very small, a special unit, called the atomic mass unit (denoted as u, or amu) is used to describe the masses. The atomic mass unit is determined as one-twelfth the mass of a carbon atom -12 and is equal to 1,66 x 10-24 grams.

• Protons, Electrons and Neutrons

Protons are positively charged particles with mass that is roughly equal to 1 amu. They are found in the center (or nucleus) of atom and have a charge of +1.6 x 10-19 Coulomb. This value of charge is known as the elementary charge and it is denoted by the symbol e.

The electrons have charge (-1,6 x 10-19 Coulomb) equal in magnitude, but different in sign (-1,6 x 10-19 Coulomb) and are found in orbits around the nucleus. In general, the electrons quantity in an atom equals to the protons number, so that the atom has no charge. An electron has a much lower mass than a proton (approximately 5 x 10-4 amu, or 1/1840 mass of a proton, or 1/1820 from the amu). This mass is so small that in order to describe the changes in the structure of atoms during radioactive decay, it can be taken as zero.

Neutrons can be regarded as a combination of proton and electron, and neutron therefore has a mass approximately equal to 1 amu, but doesn’t have the resultant electric charge. Neutrons are found in the composition of the atomic nucleus.

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• Bohr’s Atomic Model

Although the exact structure of the atom is unknown, a simple model, known as the Bohr’s atomic model (named after the physicist Niels Bohr), is used to describe the structure and properties of atoms. According to this model, the atom structure is similar to the solar system with a heavy center or nucleus (the Sun) and the lighter particles (planets) moving in orbits around the nucleus. The heavier atoms protons and neutrons form a positively charged nucleus. The lighter negatively charged electrons are drawn up to the nucleus by electrostatic forces and move in orbits around the center.

These electrons can move around the nucleus only on specific orbits called shells. There is a certain number of electrons that can be located on each shell. These shells are called K-, L-, M-, and N-shells and they can contain 2, 8, 18, and 32 electrons respectively. Note that electrons begin to fill the N-shell before the M-shell is filled. This happens because there are subshells and an overlap of energy levels. Electrons can change their orbit and move to different shells only when the atom gets energy, or releases energy.

The substance composed of the atoms of same type is called an element. The element is defined by the number of protons in each atom. Each element has its own name and symbol, as, for example, helium (He) and carbon (C).

The chemical element characteristics are determined by the number of protons (and, accordingly, the number of electrons) it contains. Neutrons have no electric charge, and therefore do not affect the chemical characteristics of the atom. However, a different number of neutrons changes the mass number of the atom, and, additionally, changes the stability of the nucleus.

## Important Atomic Concepts

Atom can be described by indicating the number of particles of which it consists. Using these definitions it is possible to uniquely identify any atom structure.

• The atomic number.
Atomic number (symbol Z) is defined as the number of protons in the nucleus and has a different value for each element. For example, for hydrogen Z equals 1, for helium Z equals 2, and for carbon Z equals 6.
• The number of neutrons.
The number of neutrons in the nucleus is denoted by the symbol –N. Although the number of neutrons for this element can be varied.
• The mass number.
The mass number is denoted by the symbol –A and is equal to the overall quantity of protons (Z) and neutrons (N) in the nucleus of an atom (the electron mass is much smaller and insignificant). The correlation between the atomic number and the quantity of protons and neutrons can be represented by the following equation: –A = Z + N. For example, the mass number of the atom of helium with two protons and two neutrons in the nucleus equals 4. And for the atom of carbon with six protons and six neutrons the mass number equals 12.

The “mass number ” is about the principle that the number of nucleons (protons and neutrons) in the nucleus almost completely (accuracy typically is better than 1%) determines the mass of atomic nucleus and atoms. Knowing the mass number helps to calculate the mass of the nucleus and the atom. If you know mass number, then the mass (M) of the atom and its nucleus is calculated from the following ratio: M ≈ A x mN, where mN is the nucleon mass, i.e. the mass of the proton or the neutron. For example, the aluminum atom and its nucleus are composed of 27 nucleons (13 protons and 14 neutrons). Its mass number will be ≈ 27 x 1.67 x 10-24g ≈ 4.5 x 10-23 g. If you want to get the more exact mass of the nucleus, you need to take into account that the nucleons in the nucleus are connected with the nuclear forces of attraction, and therefore, in accordance with the relation E = mc2, the mass of the nucleus is reduced. The mass of the atom should also contain the total mass of the electrons on orbital curves around the nucleus. However, all these corrections do not exceed 1%.

## The History of Discovering Protons, Neutrons, and the Constitution of the Atomic Nucleus

If you’re writing an argumentative essay in physics the history of discovering protons, neutrons, and the atomic nucleus construction is something you will need to mention about.

So, Rutherford in his experiments found that there is a particle called a proton. After some time in 1932, Chadwick found that there is another particle called a neutron. After this discovery, independently of each other two men, a Russian scientist Ivanenko and a German scientist Heisenberg, proposed a proton-neutron model of the structure of the atomic nucleus. According to this theory, called the theory of Ivanenko-Heisenberg, the nucleus of any atom encloses protons and neutrons. These protons and neutrons together are those that are enclosed in the nucleus of an atom, and it was decided to call them nucleons. Thus, nucleon is the word that is applied both for protons and neutrons. Those particles that have a charge and those particles that do not have a charge, neutrons, – all of these particles are collectively called nucleons.

The idea of the nucleus charge was first proposed in 1913 by the English scientist Henry Moseley. He suggested that since the atom is electrically neutral, the serial number of the element multiplied by the elementary electric charge is the charge of the nucleus. How Moseley came to that conclusion? The number of electrons in the atom corresponds to the serial number. Hence, the charge of all electrons is the product of serial number on the charge of a single electron. Since the nucleus has a positive charge, then the same can be said about the nucleus. Let’s look at how it Moseley came to what we call the atomic number: –q = Z x e, where –q is the nuclear charge, –e is the electron charge, and –Z shows the quantity of protons in the nucleus, atomic number.

Thus, when we talk about the serial number, we talk about the number of protons in the nucleus. The next important number is the mass number. This number is indicated by the letter –A, and it is taken from the periodic table and is rounded to the nearest whole number. The Ivanenko-Heisenberg equation consists of three numbers: number of mass, atomic number, and the number of neutrons: –А = Z + N.

• Isotopes

In 1913, another scientist Soddy found an interesting thing. He found that there are chemical elements with absolutely the same chemical properties, but different mass number. Such elements, which acquire the same chemical characteristics, but various mass number, became known as isotopes. Isotopes are chemical elements with the same chemical properties, but different mass of atomic nucleus. It must be added that isotopes have different radioactivity.

• Nuclear Forces

How all these particles, we have mentioned above, are held inside the nucleus? We know that only particles charged with opposite charges get attracted to each other. If the particles are charged with the same charge, it is clear that they have to push away from one another. There are positively charged protons inside the nucleus. Also, there are neutrons. So, there are forces that held together all the particles in the nucleus. These forces are called nuclear forces. Nuclear forces are forces that act between nucleons. We can say that these forces have their own special properties:

• Nuclear forces must exceed the forces of electrostatic repulsion.
• Nuclear forces operate at a short distance.
• Also, in our book report we can mention that nuclear forces are not central, i.e. they do not act along the line joining the particles.
• Nuclear forces are important in terms of nucleus stability. They are responsible for long-term survival of this element.

## The Mass number Changes in Radioactive Disintegration

Various kinds of radioactive disintegration are described by the changes in the mass number and atomic number. For example, uranium-238 generally disintegrates by alpha decay, where the nucleus loses two protons and neutrons in the form of an alpha particle. Thus, the number of neutrons and the atomic number are each decreased by two, and the mass number – by 4.

## Mass of Isotopes and Mass number

The mass number estimates the isotopic mass measured in atomic mass units. For the 12C the isotopic mass is 12, as the atomic mass unit is determined as one-twelfth of the mass. For other isotopes, the mass is usually 0.1 u of the mass number. For example, 35CI has a mass number of 35 and its isotopic mass is 34.96885.

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