13.4.1. Mass – Energy

Einstein showed from his theory of special relativity that it is necessary to treat mass as another form of energy. Before the advent of this theory of special relativity it was presumed that mass and energy were conserved separately in a reaction. However, Einstein showed that mass is another form of energy and one can convert mass-energy into other forms of energy, say kinetic energy and vice-versa.

Einstein's theory of special relativity fundamentally changed how we understand the relationship between mass and energy. It established that mass is not an unchanging quantity; rather, it is a form of energy itself. This means that in any physical process, we should consider the total energy, which includes both mass and kinetic energy. In essence, we can convert mass into energy and vice versa, highlighting a deeper connection between the two.

Think of mass and energy like water and steam. Just as water can change into steam and vice versa, mass can be converted into energy. When we burn a piece of wood, some mass is converted into energy as heat and light, similar to how steam can condense back into water.

Einstein gave the famous mass-energy equivalence relation E = mc² (13.6). Here the energy equivalent of mass m is related by the above equation and c is the velocity of light in vacuum and is approximately equal to 3×10⁸ m s⁻¹.

The equation E = mc² is one of the most famous equations in physics. It tells us that the energy (E) contained in a mass (m) is equal to that mass multiplied by the speed of light (c) squared. Since the speed of light is a very large number, even a small amount of mass can produce a huge amount of energy. For example, if you convert just 1 gram of mass into energy, it equals approximately 9 x 10¹³ joules, which is an enormous amount of energy.

Imagine a tiny battery in a toy. Although small, it can power the toy for hours. Similarly, a small amount of mass contains tremendous energy that can be released, much like how a little fire can provide a lot of heat and light.

Example 13.2 Calculate the energy equivalent of 1 g of substance. Energy, E = 10⁻³ × (3 × 10⁸)² J. E = 10⁻³ × 9 × 10¹⁶ = 9 × 10¹³ J. Thus, if one gram of matter is converted to energy, there is a release of enormous amount of energy.

In this example, we calculate how much energy can be released by converting 1 gram of mass into energy using Einstein's formula. We convert grams into kilograms (1 g = 10⁻³ kg), plug it into the equation E = mc², and get an astonishing figure of 9 x 10¹³ joules. This amount of energy is equivalent to the energy produced by burning hundreds of tons of coal, highlighting the incredible energy density of mass.

Think of 1 gram of mass as a small battery. When fully utilized, it can power a small device. If that battery could be transformed entirely into energy, it would provide a power output equivalent to thousands of batteries combined, illustrating how mass has the potential to generate vast amounts of energy.

Experimental verification of the Einstein’s mass-energy relation has been achieved in the study of nuclear reactions amongst nucleons, nuclei, electrons and other more recently discovered particles. In a reaction the conservation law of energy states that the initial energy and the final energy are equal provided the energy associated with mass is also included.

Einstein's mass-energy equivalence has been confirmed through numerous nuclear and particle physics experiments. In these reactions, scientists observe that the total energy before and after a reaction is conserved when accounting for both the standard energy forms (like kinetic and potential energy) and the energy associated with any change in mass. This underscores the principle that mass and energy are interchangeable in physical processes.

Consider playing with a rubber band. When you stretch it, you store energy in it; when you let go, that stored energy is released. In a similar way, nuclear reactions store energy in the form of mass and release it when changes occur, reaffirming the idea that mass can transform into energy, similar to how potential energy converts to kinetic energy.

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