Fr.: formule de Balmer
A special solution of the mathematical formula which represents
the wavelengths of the various spectral series of hydrogen in which the
lower energy level is n =
Fr.: formule de Bekenstein
The mathematical expression giving the → entropy, S, of a → black hole as a function of the area of its → event horizon, A: S = (kc3A)/(4Għ), where k is → Boltzmann's constant, ħ is the → reduced Planck's constant, and G the → gravitational constant. It can also be expressed by S = (kA)/(4lP2), where lP is the → Planck length. The existence of this entropy led to the prediction of the → Hawking radiation, because an entropy is associated with a temperature and a temperature to a → thermal radiation. The entropy of a black hole increases continuously because the fall of material into it increases its area.
For Jacob D. Bekenstein (1947-), an Israeli theoretical physicist, who contributed to the foundation of black hole thermodynamics; → formula.
Boltzmann's entropy formula
disul-e dargâšt-e Boltzmann
Fr.: formule d'entropie de Boltzmann
In → statistical thermodynamics, a probability equation relating the → entropy S of an → ideal gas to the quantity Ω, which is the number of → microstates corresponding to a given → macrostate: S = k. ln Ω. Same as → Boltzmann's relation.
→ Boltzmann's constant; → entropy; → formula.
compound angle formula
disul-e zaviye-ye hamnât
Fr.: formule d'angle composé
One of eight equations that give the → trigonometric functions
of → compound angles.
Fr.: formule de Descartes
A formula that gives the position of an image formed by highly → paraxial rays from a → spherical mirror. It is quite accurately given by: 1/xo + 1/xi = 2/xC, where xo is the distance along the → principal axis from the mirror to the object, xi is the distance from mirror to image, and xC is the distance from the mirror to its center of curvature. Any distance measured on the same side of the mirror as the reflecting surface is positive; on the other side, negative. Thus for a → concave mirror xC is positive; for a → convex mirror, negative.
Fr.: formule dimensionnelle
Symbolic representation of the definition of a physical quantity obtained from its units of measurement. For example, with M = mass, L = length, T = time, area = L2, velocity = LT-1, energy = ML2T-2. → dimensional analysis.
→ dimensional; → formula.
Fr.: formule empirique
1) In physics, a mathematical equation that predicts observed results, but has
no known theoretical basis to explain why it works.
Fr.: formule d'Euler
A formula which expresses an → exponential function
with an → imaginary number
→ exponent in terms of
→ trigonometric functions:
1) Physics, Math.: A statement of facts in a symbolical or general form, by
substitution in which a result applicable to particular data may be obtained.
From L. formula "form, rule, method, formula," literally "small form," from forma, → form, + → -ule diminutive suffix.
To express in precise → form; state definitely or systematically. To reduce to or express in a → formula.
Verbal form of → form.
1) The act or process of formulating.
Fr.: formule de masse
An → equation expressing the → atomic mass of a → nuclide as a function of its → mass number and the → atomic mass unit.
Fr.: formule moléculaire
The formula of a chemical compound, showing the kind and arrangement of atoms.
Fr.: formule de Newton-Leibniz
The formula expressing the value of a → definite integral of a given function over an interval as the difference of the values at the end points of the interval of any → antiderivative of the function: ∫f(x)dx = F(b) - F(a), summed from x = a to x = b.
Named after Isaac → Newton and Gottfried Wilhelm Leibniz (1646-1716), who both knew the rule, although it was published later; → formula.
Fr.: formule de Nyquist
The mean square noise voltage across a resistance in thermal equilibrium is four times the product of the resistance, Boltzmann's constant, the absolute temperature, and the frequency range within which the voltage is measured. → Johnson-Nyquist noise.
Named after Harry Nyquist (1889-1976), a Swedish-born American physicist, who made important contributions to information theory. → Johnson-Nyquist noise; → formula.
Planck's blackbody formula
disul-e siyah jesm-e Planck
Fr.: formule du corps noir de Planck
A formula that determines the distribution of intensity of radiation that prevails under conditions of thermal equilibrium at a temperature T: Bv = (2hν3 / c2)[exp(hν / kT) - 1]-1 where h is Planck's constant and ν is the frequency.
Fr.: formule quadratique
A formula relating the unknown part of a → quadratic equation (the roots of the equation, x) to the known parts (a, b, and c): x = (-b± (b2 - 4ac)½) / 2a.
Fr.: formule de Rydberg
A formula, used in atomic physics, which describes the wavelengths or frequencies of light in various series of related spectral lines, such as those emitted by hydrogen atoms.
semiempirical binding energy formula
disul-e nime-ârvini-ye kâruž-e bandeš
Fr.: formule semi-empirique de l'énérgie de liaison
Same as → Weizsacker formula.
→ semiempirical; → binding; → energy; → formula.
Fr.: formule de Weizsäcker
A → semiempirical → equation
which describes the → binding energy
of the → atomic nucleus. It is essentially a nuclear mass formula
that provides the total binding energy per → nucleon as the sum
of five terms:
Named after Carl Friedrich von Weizäcker (1912-2007), German physicist, who derived the formula in 1935, Z. für Physik 96, 431; → formula.