Assume there is one electron in a given atomic orbital in a hydrogen-like atom ( ion ).

Hence it is the atomic number alone that determines the chemical properties of an element ; and it is for this reason that an element can be defined as consisting of any mixture of atoms with a given atomic number.

Thus, the planetary model of the atom was discarded in favor of one that described atomic orbital zones around the nucleus where a given electron is most likely to be observed.

The atomic orbital concept is therefore a key concept for visualizing the excitation process associated with a given transition.

Thus the discovery report by the Berkeley group reads: " It is suggested that element 97 be given the name berkelium ( symbol Bk ) after the city of Berkeley in a manner similar to that used in naming its chemical homologue terbium ( atomic number 65 ) whose name was derived from the town of Ytterby, Sweden, where the rare earth minerals were first found.

Different isotopes of a given element are distinguished by their mass numbers, which are conventionally written as a super-index on the left hand side of the atomic symbol ( e. g., < sup > 238 </ sup > U ).

In general, it differs in value when expressed in u for a given nuclide ( or isotope ) slightly from the mass number, since the mass of the protons and neutrons is not exactly 1 u, the electrons contribute a lesser share to the atomic mass as neutron number exceeds proton number, and ( finally ) because of the nuclear binding energy.

The naming of various substances now known as elements precedes the atomic theory of matter, as names were given locally by various cultures to various minerals, metals, compounds, alloys, mixtures, and other materials, although at the time it was not known which chemicals were elements and which compounds.

In the early 1950s a Dr. Lyne Borst of Utah University was given funding by various US railroad line and manufactures to study the feasibility of an electric drive locomotive in which an on board atomic reactor produced the steam to generate the electricity.

Parting varies from crystal to crystal of a mineral, whereas all crystals of a given mineral will cleave if the atomic structure allows for that property.

The mass number of a given atomic isotope is identical to its number of nucleons.

A crude approximation, for photon energies above the highest atomic binding energy, is given by:

Planck had intentionally created an atomic theory of the black body, but had unintentionally generated an atomic theory of light, where the black body never generates quanta of light at a given frequency with an energy less than hν.

Nuclear magnetic resonance ( NMR ) is the name given to a physical resonance phenomenon involving the observation of specific quantum mechanical magnetic properties of an atomic nucleus in the presence of an applied, external magnetic field.

The discovery of isotopic oxygen in 1929 led to a divergence in atomic weight representation, with isotopically weighted oxygen ( i. e., naturally occurring oxygen atomic weight ) given a value of exactly 16 atomic mass units ( amu ) in chemistry, while pure < sup > 16 </ sup > O ( oxygen-16 ) was given the mass value of exactly 16 amu in physics.

The new and current unit was referred to as the " unified atomic mass unit " u. and given a new symbol " u ," which replaced the now deprecated " amu " that had been connected to the old oxygen-based system.

These two factors ( constancy of atomic volume and constancy of mole-specific heat capacity ) result in a good correlation between the volume of any given solid chemical element and its total heat capacity.

The unit cell is given by its lattice parameters, which are the length of the cell edges and the angles between them, while the positions of the atoms inside the unit cell are described by the set of atomic positions ( x < sub > i </ sub >, y < sub > i </ sub >, z < sub > i </ sub >) measured from a lattice point.

For example, one can say for a given transition that it corresponds to the excitation of an electron from an occupied orbital to a given unoccupied orbital.

When thinking about orbitals, we are often given an orbital vision which ( even if it is not spelled out ) is heavily influenced by this Hartree – Fock approximation, which is one way to reduce the complexities of molecular orbital theory.

In physics, the most common orbital descriptions are based on the solutions to the hydrogen atom, where orbitals are given by the product between a radial function and a pure spherical harmonic.

This explains also why the choice of z-axis for the directional quantization of the angular momentum vector is immaterial: an orbital of given ℓ and m ′ obtained for another preferred axis z ′ can always be represented as a suitable superposition of the various states of different m ( but same l ) that have been obtained for z.

Bradley explained this effect in the context of Newton's corpuscular theory of light, by showing that the aberration angle was given by simple vector addition of the Earth's orbital velocity and the velocity of the corpuscles of light, just as vertically falling raindrops strike a moving object at an angle.

A small radial impulse given to a body in orbit changes the eccentricity, but not the orbital period ( to first order ).

A calendar year is an approximation of the Earth's orbital period in a given calendar.

The applied tools of the mathematics disciplines of Celestial mechanics or its subfield Orbital mechanics ( both predict orbital paths and positions ) about a center of gravity are used to generate an ephemeris ( plural: ephemerides ; from the Greek word ephemeros = daily ) which is a table of values that gives the positions of astronomical objects in the sky at a given time or times, or a formula to calculate such given the proper time offset from the epoch.

For example, for ground stations at latitudes of φ = ± 45 ° on the same meridian as the satellite, the time taken for a signal to pass from Earth to the satellite and back again can be computed using the cosine rule, given the geostationary orbital radius r ( derived below ), the Earth's radius R and the speed of light c, as

Just as in the case of electrons, which have the lowest energy state when they occur in pairs in a given orbital, nucleons ( both protons and neutrons ) exhibit a lower energy state when their number is even, rather than odd.

There is an interaction energy associated with the magnetic dipole moment, μ < sub > L </ sub >, arising from the electronic orbital angular momentum, L, given by

The Bohr model exhibits difficulty for atoms with atomic number greater than 137, for the speed of an electron in a 1s electron orbital, v, is given by

For example, in the molecular-orbital-linear-combination-of-atomic-orbitals ( LCAO-MO ) approximation, is a molecular orbital ( MO ) given as a linear expansion of atomic orbitals ( AOs ).

The orbital elements given here are as of January 2000, but they are continuously changing due to solar and planetary perturbations.

The orbital period is the time taken for a given object to make one complete orbit about another object.

A Hohmann transfer orbit between a given circular orbit and a larger circular orbit, in the case of a single central body, costs the largest delta-v ( 53. 6 % of the original orbital speed ) if the radius of the larger orbit is 15. 58 times that of the smaller orbit.

It is much less difficult now than in Lincoln's day to see that on both sides sovereign Americans had given their lives in the Civil War to maintain the balance between the powers they had delegated to the States and to their Union.

Life is further characterized, in antithesis to Piepsam, as animal: the image of a dog, which appears at several places, is first given as the criterion of amiable, irrelevant interest aroused by life considered simply as a spectacle: a dog in a wagon is `` admirable '', `` a pleasure to contemplate '' ; ;

Their artistic rationale is given to the witness of unreason.

All such imitations of negative quality have given rise to a compensatory response in the form of a heroic and highly individualistic humanism: if man can neither know nor love reality as it is, he can at least invent an artistic `` reality '' which is its own world and which can speak to man of purely personal and subjective qualities capable of being known and worthy of being loved.

As in experience one is seized by given entities and their interrelations and is forced to respond in value feelings to them, so one is similarly seized in the mimetic presentation of images.

Whitehead contends that the human way of understanding existence as a unity of interlocking and interdependent processes which constitute each other and which cause each other to be and not to be is possible only because the basic form of such an understanding, for all its vagueness and tendency to mistake the detail, is initially given in the way man feels the world.

Since civilizational change is the most difficult to perceive and analyze, it seldom is given adequate attention.

we accord it its place there, and in Lawrence's treatment we are given the innocent fantasy of a child, in fact, the form in which oedipal love is expressed in childhood.

To innocence, a word given is a word that will be kept.

This is given some expression in Beardsley's notion of harmony and the resolution of indecision.

It is obvious that the historian who seeks to recapture the ideas that have motivated human behavior throughout a given period will find the art and literature of that age one of his central and major concerns, by no means a mere supplement or adjunct of significant historical research.

There is plenty more to recommend Gorton, the facts of whose life are given in The Life And Times Of Samuel Gorton, by Adelos Gorton.

Much more important is to grasp the feelings of the narrator ( whose full name is never given ) as he becomes aware of the disorganized and bewildered mass of French prisoners clustered together in a temporary prison camp in and around the cathedral of Chartres.

Although Patchen has given previous evidence of an interest in jazz, the musical group that he works with, the Chamber Jazz Sextet, is often ignored by jazz critics.

That such expansion can be obtained without a raise in taxes is due to growth of the tax digest and sound fiscal planning on the part of the board of commissioners, headed by Chairman Charles O. Emmerich who is demonstrating that the public trust he was given was well placed, and other county officials.

The bill which passed the Assembly last May and is now pending in the Senate should be given careful scrutiny.