Mass and Energy

The Einstein derivation

Albert Einstein derived his famous equation in 1905 in an article entitled ‘Does the inertia of a body depend upon its energy content’. Einstein describes how the emission of energy in the form of light reduces the kinetic energy of the body. His results include two important points:

Einstein’s theory only speculated that energy emission in the form of light reduced the amount of the object’s mass. However, the mass-energy equivalence can be used with respect to all forms of energy.

Mass defect and binding energy

An example of the energy-mass relationship is found in nuclear physics. Atoms are composed of particles that occur in their nucleus. These are electrons, neutrons, and protons. Each particle has its own properties, such as charge and mass. Elements that have more particles in the nucleus are, therefore, more massive and have more charge.

There is, however, a curiosity. If you take the masses of each individual particle that forms the nucleus of an element, its combined weight is larger than the mass of the element’s nucleus. The lost mass is stored in the nucleus as energy.

Mass defect

The difference between the total mass of the individual elements in the atom and the atom’s real mass is known as the mass defect. It can be expressed as follows:

\[\sum^{A-Z}_{n=1} m_n + \sum^{Z}_{p=1} m_p > \text{nuclear mass}\]

Here, m_n and m_p are the individual masses of the protons and neutrons that compose a particular atom. The total mass of the nucleus will be the sum of all neutrons and protons. The total mass of all neutrons will be the sum of the mass of each neutron m_n from n=1 to A-Z. The total mass of the protons will be the sum of the mass of each proton, m_p from n=1 to Z will be the sum of the mass of all neutrons from n=1 to A-Z. A is the mass number, while Z is the atomic number. The nuclear mass is just the mass of the atom nucleus.

As we can see, mass is lost when the nucleus is formed and stored in the form of energy, which is known as binding energy.

Binding energy

When an atom is formed, several forces are present. As we know, the particles have an electrostatic charge, and the protons are positive. Equal charges repel each other, so two protons exert a repulsive force that seeks to separate them. However, in the nucleus, protons gather alongside neutrons, which have a neutral charge.

But there is another force that binds the particles in the nucleus together. It is known as the ‘strong nuclear force’, and it acts against the electrostatic force. It is the balance between these forces in the nucleus that keeps the atom together.

The energy formed by the bonding of the particles is the binding energy, which is equal to the mass lost by the particles when the atom is formed. Thus, the mass is reduced by being converted into energy.

Reconsidering the example of the helium atom, we can calculate how much energy is equivalent to this mass by using the mass-energy equivalence equation.

It is normal for these reactions to be expressed as electron volts, which makes calculations easier, as 1 amu is equal to 931.5 MeV.

Applications of the mass-energy equivalence

One of the main applications of the mass-energy equivalence is in nuclear energy and nuclear reactions. During the process of fission, heavy atoms break into smaller particles and elements. This process is known as nuclear decay, and it releases energy from the atom itself.

Nuclear Fission

Nuclear fission is an atomic reaction during which heavy elements break away, releasing neutrons that are trapped by other heavy elements. The breakaway produces smaller elements and releases free particles as well as large amounts of energy, which can be used to heat a working fluid (usually water) and produce high-pressure steam that is directed towards a steam turbine connected to an electrical generator.

The process in which a fission reaction occurs is a chain reaction. In this kind of reaction, many atoms of heavy unstable elements are packed together. Some of these elements decay naturally and release energy while breaking into smaller pieces, some of which are neutrons. The free neutrons impact other atoms, inducing more breakaways and increasing the amount of energy released in this chain reaction.

The process is controlled by another material that can absorb electrons, reducing their number and making the fission reaction decay.

Some uses of fission include:

• Production of energy by nuclear reactors.
• Production of isotopes used in medicine and tracing technologies.
• Production of isotopes used in space applications, such as plutonium.