भौतिक नियतांक

मुक्त ज्ञानकोश विकिपीडिया से
यहाँ जाएँ: भ्रमण, खोज

भौतिक नियतांक (physical constant) उस भौतिक राशि (physical quantity) को कहते हैं जिसके बारे में ऐसा विश्वास किया जाता है कि वह राशि प्रकृति में सार्वत्रिक (universal) है तथा समय के साथ अपरिवर्तनशील या नियत है। भौतिक नियतांक, गणितीय नियतांक से इस मामले में भिन्न हैं कि गणितीय नियतांक संख्यात्मक दृष्टि से तो नियत होते हैं किन्तु उनका किसी मापन से सम्बन्ध नहीं होता।

विज्ञान में बहुत से भौतिक नियतांक हैं जिनमें से प्रमुख हैं - शून्य में प्रकाश का वेग c, गुरुत्वाकर्षण नियतांक G, प्लांक नियतांक h, निर्वात का विद्युत नियतांक ε0, तथा एलेक्ट्रान का आवेश e.

विमासहित एवं विमारहित भौतिक नियतांक ( Dimensionful and dimensionless physical constants)[संपादित करें]

विस्तृत जानकारी के लिये मूलभूत भौतिक नियतांक देखें ।

सार्वत्रिक नियतांकों की सारणी[संपादित करें]

Quantity Symbol Value Relative Standard Uncertainty
speed of light in vacuum c \, 299 792 458 m·s−1 defined
Newtonian constant of gravitation G \, 6.67428(67)×१०−11 m3·kg−1·s−2 1.0 × 10−4
Planck constant h \, 6.626 068 96(33) × 10−34 J·s 5.0 × 10−8
reduced Planck constant \hbar = h / (2 \pi) 1.054 571 628(53) × 10−34 J·s 5.0 × 10−8

विद्युतचुम्बकीय नियतांकों की सारणी[संपादित करें]

Quantity Symbol Value[1] (SI units) Relative Standard Uncertainty
magnetic constant (vacuum permeability)  \mu_0 \, 4π × 10−7 N·A−2 = 1.256 637 061... × 10−6 N·A−2 defined
electric constant (vacuum permittivity)  \varepsilon_0 = 1/(\mu_0 c^2) \, 8.854 187 817... × 10−12 F·m−1 defined
characteristic impedance of vacuum Z_0 = \mu_0 c \, 376.730 313 461... Ω defined
Coulomb's constant \kappa = 1 / 4\pi\epsilon_0 \, 8.987 551 787... × 109 N·m²·C−2 defined
elementary charge e
\, 1.602 176 487(40) × 10−19 C 2.5 × 10−8
Bohr magneton \mu_B = e \hbar / 2 m_e 927.400 915(23) × 10−26 J·T−1 2.5 × 10−8
conductance quantum G_0 = 2 e^2 / h \, 7.748 091 7004(53) × 10−5 S 6.8 × 10−10
inverse conductance quantum G_0^{-1} = h / 2 e^2 \, 12 906.403 7787(88) Ω 6.8 × 10−10
Josephson constant K_J = 2 e / h \, 4.835 978 91(12) × 1014 Hz·V−1 2.5 × 10−8
magnetic flux quantum \phi_0 = h / 2 e \, 2.067 833 667(52) × 10−15 Wb 2.5 × 10−8
nuclear magneton \mu_N = e \hbar / 2 m_p 5.050 783 43(43) × 10−27 J·T−1 8.6 × 10−8
von Klitzing constant R_K = h / e^2 \, 25 812.807 557(18) Ω 6.8 × 10−10

परमाणवीय एवं नाभिकीय नियतांकों की सारणी[संपादित करें]

Quantity Symbol Value[1] (SI units) Relative Standard Uncertainty
Bohr radius a_0 = \alpha / 4 \pi R_\infin \, 5.291 772 108(18) × 10−11 m 3.3 × 10−9
classical electron radius r_e = e^2 / 4\pi\epsilon_0 m_e c^2\, 2.817 940 2894(58) × 10−15 m 2.1 × 10−9
electron mass m_e \, 9.109 382 15(45) × 10−31 kg 5.0 × 10−8
Fermi coupling constant G_F / (\hbar c)^3 1.166 39(1) × 10−5 GeV−2 8.6 × 10−6
fine-structure constant \alpha = \mu_0 e^2 c / (2 h) = e^2 / (4 \pi \epsilon_0 \hbar c) \, 7.297 352 537 6(50) × 10−3 6.8 × 10−10
Hartree energy E_h = 2 R_\infin h c \, 4.359 744 17(75) × 10−18 J 1.7 × 10−7
proton mass m_p \, 1.672 621 637(83) × 10−27 kg 5.0 × 10−8
quantum of circulation h / 2 m_e \, 3.636 947 550(24) × 10−4 m² s−1 6.7 × 10−9
Rydberg constant R_\infin = \alpha^2 m_e c / 2 h \, 10 973 731.568 525(73) m−1 6.6 × 10−12
Thomson cross section (8 \pi / 3)r_e^2 6.652 458 73(13) × 10−29 2.0 × 10−8
weak mixing angle \sin^2 \theta_W = 1 - (m_W / m_Z)^2 \, 0.222 15(76) 3.4 × 10−3

भौतिक-रासायनिक नियतांकों की सारणी[संपादित करें]

Quantity Symbol Value[1] (SI units) Relative Standard Uncertainty
atomic mass unit (unified atomic mass unit) m_u = 1 \ u \, 1.660 538 86(28) × 10−27 kg 1.7 × 10−7
Avogadro's number N_A, L \, 6.022 141 5(10) × 1023 mol−1 1.7 × 10−7
Boltzmann constant k = k_B = R / N_A \, 1.380 6504(24) × 10−23 J·K−1 1.8 × 10−6
Faraday constant F = N_A e \, 96 485.3383(83)C·mol−1 8.6 × 10−8
first radiation constant c_1 = 2 \pi h c^2 \, 3.741 771 18(19) × 10−16 W·m² 5.0 × 10−8
for spectral radiance c_{1L} \, 1.191 042 82(20) × 10−16 W·m² sr−1 1.7 × 10−7
Loschmidt constant at T=273.15 K and p=101.325 kPa n_0 = N_A / V_m \, 2.686 777 3(47) × 1025 m−3 1.8 × 10−6
gas constant R \, 8.314 472(15) J·K−1·mol−1 1.7 × 10−6
molar Planck constant N_A h \, 3.990 312 716(27) × 10−10 J·s·mol−1 6.7 × 10−9
molar volume of an ideal gas at T=273.15 K and p=100 kPa V_m = R T / p \, 2.2710 981(40) × 10−2 m³·mol−1 1.7 × 10−6
at T=273.15 K and p=101.325 kPa 2.2413 996(39) × 10−2 m³·mol−1 1.7 × 10−6
Sackur-Tetrode constant at T=1 K and p=100 kPa S_0 / R = \frac{5}{2}
 + \ln\left[ (2\pi m_u k T / h^2)^{3/2} k T / p \right]
−1.151 704 7(44) 3.8 × 10−6
at T=1 K and p=101.325 kPa −1.164 867 7(44) 3.8 × 10−6
second radiation constant c_2 = h c / k \, 1.438 775 2(25) × 10−2 m·K 1.7 × 10−6
Stefan-Boltzmann constant \sigma = (\pi^2 / 60) k^4 / \hbar^3 c^2 5.670 400(40) × 10−8 W·m−2·K−4 7.0 × 10−6
Wien displacement law constant b = (h c / k) /   \, 4.965 114 231... 2.897 768 5(51) × 10−3 m·K 1.7 × 10−6

स्वीकृत मानों की सारणी (Table of adopted values)[संपादित करें]

Quantity Symbol Value (SI units) Relative Standard Uncertainty
conventional value of Josephson constant[2] K_{J-90} \, 4.835 979 × 1014 Hz·V−1 defined
conventional value of von Klitzing constant[3] R_{K-90} \, 25 812.807 Ω defined
molar mass constant M_u = M(\,^{12}\mbox{C}) / 12 1 × 10−3 kg·mol−1 defined
of carbon-12 M(\,^{12}\mbox{C}) = N_A m(\,^{12}\mbox{C}) 1.2 × 10−2 kg·mol−1 defined
standard acceleration of gravity (gee, free-fall on Earth) g_n \,\! 9.806 65 m·s−2 defined
standard atmosphere  \mbox{atm} \, 101 325 Pa defined

प्राकृतिक इकाइयाँ[संपादित करें]

Using dimensional analysis, it is possible combine fundamental physical constants to produce basic units of measurement. Depending on the choice and arrangement of constants used, the resulting natural units may have physical meaning. For example, Planck units use c, G, \hbar , \epsilon_0 and k to derive constants relevant to unified theories, including quantum gravity.

Name Dimension Expression Value[1] (SI units)
Planck length Length (L) l_\text{P} = \sqrt{\frac{\hbar G}{c^3}} 1.616 252(81) × 10−35 m
Planck mass Mass (M) m_\text{P} = \sqrt{\frac{\hbar c}{G}} 2.176 44(11) × 10−8 kg
Planck time Time (T) t_\text{P} = \sqrt{\frac{\hbar G}{c^5}} 5.391 24(27) × 10−44 s
Planck charge Electric charge (Q) q_\text{P} = \sqrt{4 \pi \varepsilon_0 \hbar c} 1.875 545 870(47) × 10−18 C
Planck temperature Temperature (Θ) T_\text{P} = \sqrt{\frac{\hbar c^5}{G k^2}} 1.416 785(71) × 1032 K

टिप्पणियाँ[संपादित करें]

  1. The values are given in the so-called concise form; the number in brackets is the standard uncertainty, which is the value multiplied by the relative standard uncertainty.
  2. This is the value adopted internationally for realizing representations of the volt using the Josephson effect.
  3. This is the value adopted internationally for realizing representations of the ohm using the quantum Hall effect.

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