Displaying 31-40 of 53 results found.
Decimal expansion of h^2, where h is the Planck constant in SI units.
+0
1
4, 3, 9, 0, 4, 8, 0, 5, 6, 3, 2, 7, 2, 1, 0, 2, 2, 5
EXAMPLE
h^2 = 4.390 480 563 272 102 25 * 10^(-67).
Decimal expansion of G*h^2/c^4 in SI units, where G is the Newtonian constant of gravitation, h is the Planck constant and c is the speed of light in vacuum.
+0
0
COMMENTS
Also decimal expansion of h^2/F_P in SI units, where h is the Planck constant and F_P is the Planck force.
According to the law of universal gravitation, the attractive force (F) between two bodies is proportional to the product of their masses (m_1 and m_2), and inversely proportional to the square of the distance, r, between them. Newton's formula is F = G*m_1*m_2/r^2, where G is the constant of gravitation. Using both the Planck force (F_P) and Einstein's formula E = m*c^2, the law of universal gravitation could be written as F = (G/c^4)*m_1*c^2*m_2*c^2/r^2, or, more simply, F = (1/F_P)*E_1*E_2/r^2, where both E_1 and E_2 are the energies of the bodies.
Then using the Einstein's formula E = m*c^2 and the Planck-Einstein relation E = h*f, the law of universal gravitation between two photons could be written as F = (G*h^2/c^4)*f_1*f_2/r^2, or simply, F = (h^2/F_P)*f_1*f_2/r^2, or, more simply, F = Q*f_1*f_2/r^2, where both f_1 and f_2 are the frequencies of the photons and Q is this constant. (End)
EXAMPLE
Q = 3.627... * 10^-111 [kg * m^3].
Decimal expansion of 4/h, where h is the Planck constant in SI units.
+0
0
COMMENTS
The Margolus-Levitin theorem says that the limit of elementary operations that a physical system can perform is ~ 6.03676 * 10^33 operations per second per joule of energy.
EXAMPLE
6.03676 * 10^33 Joule * second.
Decimal expansion of the hyperfine transition of neutral hydrogen in Hertz.
+0
1
1, 4, 2, 0, 4, 0, 5, 7, 5, 1, 7, 6
REFERENCES
Ludwig Bergmann, Clemens Schaefer (edited by Wilhelm Raith), Constituents of Matter: Atoms, Molecules, Nuclei, and Particles, Walter de Gruyter & Co., Berlin, 1997, p. 203.
FORMULA
Equals E * A081823 / A003676, where E is the energy (in eV) emitted after spin-flip transition of atomic hydrogen in its ground electronic state.
EXAMPLE
1420405751.7667 +- 0.0009 Hz.
Decimal expansion of the second radiation constant c_2 in meter-kelvin.
+0
0
1, 4, 3, 8, 7, 7, 6, 8, 7, 7, 5, 0, 3, 9, 3, 3, 8, 0, 2, 1, 4, 6, 6, 7, 1, 6, 0, 1, 5, 4, 3, 9, 1, 1, 5, 9, 5, 1, 9, 9, 0, 6, 9, 4, 2, 3, 1, 4, 8, 0, 9, 9, 1, 9, 1, 0, 3, 2, 6, 2, 3, 0, 6, 3, 5, 0, 1, 2, 9, 5, 4, 0, 5, 2, 7, 6, 7, 9, 3, 7, 3, 9, 7, 5, 5, 7, 2
COMMENTS
Appears as a term in the Sakuma-Hattori equation for the electromagnetic signal from the thermal radiation emitted by an ideal black body of a given temperature.
The exact value, following the 2019 redefinition of SI units, is 272115870842319/18913000000000000. Hence, periodic with period 18912. - Charles R Greathouse IV, Jun 25 2021
FORMULA
c_2 = h*c/k where k is Planck's constant, c is the speed of light in a vacuum, and k is the Boltzmann constant. - Charles R Greathouse IV, Jun 25 2021
EXAMPLE
0.014387768775039338021466716015439115951990694231480991910326230635012954... m K.
PROG
(PARI) period(r, base=10)=
{
my(d=denominator(r), f=factor(base)[, 1]);
for(i=1, #f,
d /= f[i]^valuation(d, f[i])
);
znorder(Mod(base, d));
}
rationalNumberOrder(r, base=10)=
{
my(f=factor(base)[, 1], t, L, x='x, P);
for(i=1, #f,
t=valuation(r, f[i]);
if(t<0, r*=f[i]^-t)
);
r = frac(r);
L = period(r, base);
P = Polrev(digits(r*(base^L-1)));
poldegree(denominator(P/(1-x^L)));
}
Decimal expansion of quantum of circulation in m^2 s^(-1).
+0
0
COMMENTS
Equal to half the ratio of the Planck constant to the mass of the electron, i.e., (1/2)* A003676/ A081801.
EXAMPLE
3.6369475486(17)*10^(-4) m^2 s^(-1).
Decimal expansion of h * Δν_{Cs} / c^2 in units of kg in the 2019 SI system of units.
+0
16
6, 7, 7, 7, 2, 6, 5, 3, 1, 2, 3, 1, 2, 0, 6, 7, 6, 1, 0, 6, 1, 7, 2, 7, 0, 2, 3, 4, 6, 5, 8, 4, 3, 5, 5, 3, 9, 4, 4, 6, 4, 5, 5, 7, 0, 6, 2, 4, 2, 3, 2, 3, 9, 8, 0, 4, 2, 6, 6, 2, 2, 4, 5, 0, 7, 0, 9, 9, 8, 6, 1, 7, 6, 7, 8, 8
COMMENTS
The seven defining constants of the SI system (May 20 2019) are (see the BIPM link):
Δν_{Cs} = Δν(133Cs)_{hfs} = 9192631770 s^(-1)
c = 299792458 m/s
h = 6.62607015*10^{-34} J s [kg m^2 s^(-1)]
e = 1.602176634*10^{-19} C [A s]
k = 1.380649*10^{-23} J/K [kg m^2 s^(-2) K^(-1)]
N_A = 6.02214076*10{23} mol^(-1)
K_{cd} = 683 lm/W [cd sr s^3 kg^(-1) m^(-2)]
In brackets are the units given in s, m, kg, A, K, and cd*sr. The symbol sr stands for steradian (or sterad).
K_{cd} is the luminous efficacy of monochromatic radiation of frequency 540*10^12 Hz, with Hz = 1/s.
The given combination of three constants defines the kg from the Planck constant h after s and m have been expressed in terms of Delta nu_{Cs} and c.
FORMULA
Equals 0.677726531231206761061727023465843553944645570624232398042662245... * 10^{-40} kg.
CROSSREFS
Cf. A230458 (Δν_{Cs}), A003678 (c) A003676 (h), A081823 (e), A070063 (k), A248510 (R_K), A248508 (K_{J}), A322579 (m), A322580 (kg), A324031 (A), A324032 (K), A324033 (lm), A324034 (J).
Decimal expansion of the Avogadro constant N_A in the 2019 SI system in units mol^(-1).
+0
14
6, 0, 2, 2, 1, 4, 0, 7, 6
COMMENTS
The Avogadro comstant N_A is one of the seven units of the 2019 SI system of units. See the BIMP link with the CGPM resolutions which become effective om May 20 2019. See also A322415. This is also the conversion factor of the old SI unit mol into the reciprocal 2010 SI unit 1/N_A.
LINKS
BIPM, CGPM-2018 [See the link "Resolutions of the CGPM" there.]
FORMULA
N_A = 6.02214076×10^23 mol^(-1) = 2^17*5^15*563*267413 mol^(-1).
Decimal expansion of the conversion factor from the old SI unit kg to the combination of 2019 SI units h*Δν_{Cs}/c^2.
+0
2
1, 4, 7, 5, 5, 2, 1, 3, 9, 9, 7, 3, 5, 2, 7, 0, 9, 1, 6, 0, 6, 5, 0, 2, 5, 9, 5, 3, 6, 2, 2, 1, 2, 4, 1, 5, 6, 3, 8, 9, 0, 5, 9, 6, 9, 2, 4, 9, 7, 2, 8, 3, 5, 2, 0, 0, 2, 2, 8, 2, 4, 7, 6, 8, 7, 2, 3, 9, 8, 2, 7, 3, 9, 2, 9, 8, 7, 3, 0, 9, 3, 7, 6, 0, 2, 6, 5, 6, 4, 0, 2, 8, 5, 9, 1, 1, 6, 2, 3, 1, 4, 1, 6
COMMENTS
For the seven units of the 2019 SI system of units see the BIPM link with the resolutions of the CGPM, and A322415.
LINKS
BIPM, CGPM-2018 [See the link "Resolutions of the CGPM" there.]
FORMULA
1kg = (299792458)^2/(662607015*9192631770) * 10^{42} h*Delta nu_{Cs}/c^2
1 kg = 1.47552139973527091606502595362212415638905969249728352002282476872398273... * 10^40 h*Δν_{Cs}/c^2.
Decimal expansion of the conversion factor from the old SI K (kelvin) to the combination of 2019 SI units h*Δν_{Cs}/k.
+0
1
2, 2, 6, 6, 6, 6, 5, 2, 6, 4, 6, 0, 1, 1, 0, 4, 8, 6, 7, 3, 6, 0, 1, 0, 8, 1, 4, 7, 3, 6, 2, 0, 6, 6, 3, 5, 6, 9, 7, 4, 3, 6, 7, 1, 8, 0, 4, 6, 6, 3, 9, 3, 0, 7, 1, 7, 6, 4, 0, 7, 8, 5, 0, 5, 9, 9, 8, 2, 5, 8, 7, 1, 9, 8, 6, 8, 7, 5, 0, 2, 1, 5, 0, 7, 4, 7, 6, 2, 3, 4, 7, 2, 7, 2, 0, 1, 4, 4, 3, 6, 7, 4, 0, 3
COMMENTS
For the seven units of the 2019 SI system of units see the BIPM link with the resolutions of the CGPM, and A322415.
LINKS
BIPM, CGPM-2018 [See the link "Resolutions of the CGPM" there.]
FORMULA
1 K = 1.380649/(6.62607015*9192631770) x 10^{11} h*Δν_{Cs}/k.
1 K = 2.2666652646011048673601081473620663569743671804663930... h*Δν_{Cs}/k.
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