Rest energy in the context of "Energy transfer"

Energy (from Ancient Greek ἐνέργεια (enérgeia) 'activity') is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule (J).

Forms of energy include the kinetic energy of a moving object, the potential energy stored by an object (for instance due to its position in a field), the elastic energy stored in a solid object, chemical energy associated with chemical reactions, the radiant energy carried by electromagnetic radiation, the internal energy contained within a thermodynamic system, and rest energy associated with an object's rest mass. These are not mutually exclusive.

In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or a material medium. This includes:

• electromagnetic radiation consisting of photons, such as radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and gamma radiation (γ)
• particle radiation consisting of particles of non-zero rest energy, such as alpha radiation (α), beta radiation (β), proton radiation and neutron radiation
• acoustic radiation, such as ultrasound, sound, and seismic waves, all dependent on a physical transmission medium
• gravitational radiation, in the form of gravitational waves, ripples in spacetime

Radiation is often categorized as either ionizing or non-ionizing depending on the energy of the radiated particles. Ionizing radiation carries more than 10 electron volts (eV), which is enough to ionize atoms and molecules and break chemical bonds. This is an important distinction due to the large difference in harmfulness to living organisms. A common source of ionizing radiation is radioactive materials that emit α, β, or γ radiation, consisting of helium nuclei, electrons or positrons, and photons, respectively. Other sources include X-rays from medical radiography examinations and muons, mesons, positrons, neutrons and other particles that constitute the secondary cosmic rays that are produced after primary cosmic rays interact with Earth's atmosphere.

The word "mass" has two meanings in special relativity: invariant mass (also called rest mass) is an invariant quantity which is the same for all observers in all reference frames, while the relativistic mass is dependent on the velocity of the observer. According to the concept of mass–energy equivalence, invariant mass is equivalent to rest energy, while relativistic mass is equivalent to relativistic energy (also called total energy).

The term "relativistic mass" tends not to be used in particle and nuclear physics and is often avoided by writers on special relativity, in favor of referring to the body's relativistic energy. In contrast, "invariant mass" is usually preferred over rest energy. The measurable inertia of a body in a given frame of reference is determined by its relativistic mass, not merely its invariant mass. For example, photons have zero rest mass but contribute to the inertia (and weight in a gravitational field) of any system containing them.

The Compton wavelength is a quantum mechanical property of a particle, defined as the wavelength of a photon whose energy is the same as the rest energy of that particle (see Mass–energy equivalence). It was introduced by Arthur Compton in 1923 in his explanation of the scattering of photons by electrons (a process known as Compton scattering).

The standard Compton wavelength λ of a particle of mass m is given by$${\displaystyle \lambda ={\frac {h}{mc}},}$$where h is the Planck constant and c is the speed of light.The corresponding frequency f is given by$${\displaystyle f={\frac {mc^{2}}{h}},}$$ and the angular frequency ω is given by$${\displaystyle \omega ={\frac {mc^{2}}{\hbar }}.}$$