From a relativistic point of view, mass-energy is the total amount of energy of a body as expressed in Einstein’s E = mc2.
Individual particles may have mass. The electron is often said to have no mass but actually has a small amount: 1/1,836 that of a proton. To be precise, the mass of an electron is 9.10938291 × 10-31 kg. The electron’s small mass means a tiny force can accelerate it to a high speed.
By convention, photons are considered to be massless. But photons do possess energy and according to Einstein’s theory of Relativity, backed up by ample experiment and observation, energy and mass are related by E = mc2. According to this equation, photons do indeed have a certain mass.
Notwithstanding, it is generally said that the photon is totally without mass. Were it to have a definite mass, it would not move at the “speed of light” in a vacuum. It would travel at a lower speed dependent upon frequency. With any mass at all, light particles would travel at the speed of gravitons.
The mass of a proton is 1.67262178 × 10-27 kg. While much more massive than an electron or the ghostly photon, this is still a tiny number.
Because it has no charge, the mass of a neutron cannot be measured by means of mass spectrometry. It is considered to be slightly greater than the mass of a proton.
Besides mass, one of the attributes often but not always exhibited by atomic particles and matter is charge. It is defined as a property of matter that makes it experience a force when placed in a magnetic field. Besides being influenced by electromagnetic fields, electrically charged matter also produces them.
As ancients discovered and children with inquiring minds quickly learn, unlikes attract and likes repel one another. This is true of both magnets and electrically charged objects.
The basic unit of charge is the electron, and it is considered to be negative, although this is a matter of semantics. Because electrical current consists of a flow of electrons, it might be more appropriate to consider the electron as carrying a positive charge, but it is too late for that.
In line with quantum physics, it has been amply demonstrated that the unit of electrical charge is quantized. What this means is that at the small end of things there exists a minimum electrical charge that cannot be further subdivided, although this statement must be modified in the strange case of the quark.
For the most part, charge on a macro scale exists in integer multiples of the elementary charge, denoted e, which is approximately 1.602 × 10-19 coulombs. Quarks carry charges that are integer multiples of e/3. Because single quarks do not exist in nature, the fundamental quantum unit of charge may be allowed to stand.
Robert Millikan is credited with determining the exact electrical charge of an electron. He measured the speed of water droplets through an electric field. Finding that water evaporated too quickly, he later substituted oil drops. He found the charge on the droplets was always a multiple of a single amount, and by simple division the elementary charge was found.
The electron, again by convention, defines the elementary charge as –e. In line with this, the elementary charge of a proton is +e. Because of their mutual attraction, the electron remains in orbit around an atom’s nucleus. Protons, despite their like charges, remain tightly bound together in the nucleus of an atom, thanks to their strong attraction to the neutrons. The atomic nucleus remains stable unless otherwise persuaded by the gentle ministrations of atomic weapon makers or producers of the energy that converts water to steam in order to power turbines and ultimately electrical generators.
A third property, spin, is still more elusive. The basic concept is familiar. We all know that the earth, like many spherical bodies, turns on its axis. It is said to have angular momentum that does not change, slow down or speed up, unless force or friction is applied.
This angular momentum principle is illustrated by that wonderful nineteenth-century mechanism, the centrifugal fly-ball governor, used to regulate a steam engine’s speed of rotation. Any change in angular momentum will let the weighted spheres move upward or downward toward the center of the earth, making for change in RPM. Linkage to a steam intake valve adjusts engine torque to regulate speed.
All of this is in accord with Newtonian physics. But in the quantum realm of the super small, the situation with regard to spin is altogether different. A simplistic notion would be to conceive of elementary particles as rotating about their axes much like astronomical bodies such as the earth. This is true in that the mathematical laws that are applicable to quantized angular momentum are valid. But there are differences between these phenomena.
The direction of an elementary particle’s spin can change, but the speed of rotation for any given elementary particle is fixed, and that is what determines the quantum number. Depending on the type of particle, the quantum number may be expressed as half-integer values.
Bosons have integer spins, such as 0, 1 and 2. Fermions have half-integer spins, such as 1/2, 3/2 and 5/2. Fermions conform to the Pauli exclusion principle. Bosons do not, meaning that two bosons may have the same time and space co-ordinates.
By definition, true elementary particles such as the electron cannot be further subdivided. Accordingly, spin must be seen as an intrinsically basic physical property, in the same category as mass and charge.
But whereas mass and charge accrete when elementary particles join to work in concert, spin is quite different. The spin of a composite particle, such as a helium atom, is different from that of the elementary particles from which it is formed. A helium atom can have an integer spin 0, becoming in effect a boson, despite the fact that its components — electrons and quarks — have half-integer spins and thus are fermions.
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