Einstein's Mass-Energy Equivalence - Learn

Einstein’s Mass-Energy Equivalence – Learn

The result of special relativity is the equivalence of mass and energy. Einstein concluded that energy and mass are equivalent – mass can be converted into energy and energy can be converted into mass. The energy associated with the mass at rest is called the rest energy. This is quantified in the equation:

$E\:=\:m{ c }^{ 2 }$

where:

$E$ is the rest energy in J (or eV by conversion: 1eV = 1.602 × 10⁻¹⁹ J)

$m$ is the mass in kg

$c$ is the speed of light – 3 × 10⁸ m/s

Production of Energy by the Sun

Fusion reactions take place in the Sun that create larger atoms and nuclei. During fusion reactions, there will be a mass defect – a loss in mass as a result of the nuclear reaction. This mass defect will result in large amounts of energy being released. The energy released is in accordance with Einstein’s equation: $E\:=\:m{ c }^{ 2 }$

The main reaction that takes place in the Sun is the fusion of hydrogen nuclei to form helium. Every second, approximately 657 tonnes of hydrogen nuclei and hydrogen isotopes are converted into 653 tonnes of helium. This results in a mass defect of 4 tonnes EVERY second. This mass defect is converted into the energy that gets released every second from the Sun.

Particle–Antiparticle Interactions, eg positron–electron annihilation

A positron is the antiparticle of an electron. It has the same mass as an electron and a positive charge that is equal in magnitude. Positrons are produced when proton-rich radioactive nuclei decay as the result of a proton decaying into a neutron.

If a positron collides with an electron with low energy (slower speed) annihilation occurs and energy is released in the form of gamma rays:

$_{ -1 }^{ \quad 0 }{ e }\:+\:_{ +1 }^{ \quad 0 }{ e }\:\rightarrow\: \gamma \:+\:\gamma$

During this annihilation process, charge is conserved and so is the total mass. According to Einstein, mass is a measure of the energy content of the object – this energy is represented by Einstein’s equation. The mass of the electron and positron are converted into the energy of the gamma rays.

Combustion of Conventional Fuel

The examples above deal with nuclear reactions – nuclear reactions release huge amounts of energy. Einstein’s equation, $E\:=\:m{ c }^{ 2 }$ , also applies to chemical reactions. The energy released during a chemical reaction can be used to calculate any change in mass. Any loss in mass during a chemical reaction is very small and often goes unnoticed

Example:

How much energy is released during an electron-positron annihilation? The rest mass of an electron and a positron is 9.1 × 10⁻³¹ kg.

using the nuclear equation: $_{ -1 }^{ \quad 0 }{ e }\:+\:_{ +1 }^{ \quad 0 }{ e }\:\rightarrow\: \gamma \:+\:\gamma$ and $E\:=\:m{ c }^{ 2 }$ :

$E=2\times (9.1\times { 10 }^{ -31 })\times (3\times { 10 }^{ 8 })^{ 2 }$

$E=1.638\times { 10 }^{ -12 }\:J$

$E=1.02\:MeV$