PHY01, Physical constant and unit and equation
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Contents
- Some Physical Constant
- Some Prefixes for Powers of Ten
- Systems of Units
- SI-Unit : Fundamental Unit
- SI-Unit : Derived Unit
- Symbols, Dimensions, and Units of Physical Quantities
- Equations
Some Physical Constant
| Quantity | Symbol | Value |
|---|---|---|
| Atomic mass unit | \(u\) | \(1.66053886(28)\times 10^{ -27 }\ kg\) \(931.494043(80)\ MeV/c^{ 2 }\) |
| Avogadro’s number | \(N_{ A }\) | \(6.0221415(10)\times 10^{ 23 }\ particles/mol\) |
| Bohr magneton | \(\mu _{ B }=\frac { e\hbar }{ 2m_{ e } }\) | \(9.27400949(80)\times 10^{ -24 }\ J/T\) |
| Bohr radius | \(a_{ 0 }=\frac { \hbar ^{ 2 } }{ m_{ e }e^{ 2 }k_{ e } }\) | \(5.291772108(18)\times 10^{ -11 }\ m\) |
| Boltzmann’s constant | \(k_{ B }=\frac { R }{ N_{ A } }\) | \(1.3806505(24)\times 10^{ -23 }\ J/K\) |
| Compton wavelength | \(\lambda _{ C }=\frac { h }{ m_{ e }c }\) | \(2.426310238(16)\times 10^{ -12 }\ m\) |
| Coulomb constant | \(k_{ e }=\frac { 1 }{ 4\pi \varepsilon _{ 0 } }\) | \(8.987551788...\times 10^{ 9 }\ N\cdot m^{ 2 }/C^{ 2 }\) |
| Deuteron mass | \(m_{ d }\) | \(3.34358335(57)\times 10^{ -27 }\ kg\) \(2.01355321270(35)\ u\) |
| Electron mass | \(m_{ e }\) | \(9.1093826(16)\times 10^{ -31 }\ kg\) \(5.4857990945(24)\times 10^{ -4 }\ u\) \(0.510998918(44)\ MeV/c^{ 2 }\) |
| Electron volt | \(eV\) | \(1.60217653(14)\times 10^{ -19 }\ J\) |
| Elementary charge | \(e\) | \(1.60217653(14)\times 10^{ -19 }\ C\) |
| Gas constant | \(R\) | \(8.314472(15)\ J/mol\cdot K\) |
| Gravitational constant | \(G\) | \(6.6742(10)\times 10^{ -11 }\ N\cdot m^{ 2 }/kg^{ 2 }\) |
| Josephson frequency – voltage ratio | \(\frac { 2e }{ h }\) | \(4.83597879(41)\times 10^{ 14 }\ Hz/V\) |
| Magnetic flux quantum | \(\Phi _{ 0 }=\frac { h }{ 2e }\) | \(2.06783372(18)\times 10^{ -15 }\ T\cdot m^{ 2 }\) |
| Neutron mass | \(m_{ n }\) | \(1.67492728(29)\times 10^{ -27 }\ kg\) \(1.00866491560(55)\ u\) \(939.565360(81)\ MeV/c^{ 2 }\) |
| Nuclear magneton | \(\mu _{ n }=\frac { e\hbar }{ 2m_{ p } }\) | \(5.05078343(43)\times 10^{ -27 }\ J/T\) |
| Permeability of free space | \(\mu _{ 0 }\) | \(4\pi \times 10^{ -7 }\ T\cdot m/A\) |
| Permittivity of free space | \(\varepsilon _{ 0 }=\frac { 1 }{ \mu _{ 0 }c^{ 2 } }\) | \(8.854187817...\times 10^{ -12 }\ C^{ 2 }/N\cdot m^{ 2 }\) |
| Planck’s constant | \(h\) \(\hbar =\frac { h }{ 2\pi }\) |
\(6.6260693(11)\times 10^{ -34 }\ J\cdot s\) \(1.05457168(18)\times 10^{ -34 }\ J\cdot s\) |
| Proton mass | \(m_{ p }\) | \(1.67262171(29)\times 10^{ -27 }\ kg\) \(1.00727646688(13)\ u\) \(938.272029(80)\ MeV/c^{ 2 }\) |
| Rydberg constant | \(R_{ H }\) | \(1.0973731568525(73)\times 10^{ 7 }\ m^{ -1 }\) |
| Speed of light in vacuum | \(c\) | \(2.99792458\times 10^{ 8 }\ m/s\) |
Some Prefixes for Powers of Ten
| Power | Prefix | Abbreviation | Power | Prefix | Abbreviation |
|---|---|---|---|---|---|
| \(10^{-24}\) | yocto | \(y\) | \(10^{1}\) | deca | \(da\) |
| \(10^{-21}\) | zepto | \(z\) | \(10^{2}\) | hecto | \(h\) |
| \(10^{-18}\) | atto | \(a\) | \(10^{3}\) | kilo | \(k\) |
| \(10^{-15}\) | femto | \(f\) | \(10^{6}\) | mega | \(M\) |
| \(10^{-12}\) | pico | \(p\) | \(10^{9}\) | giga | \(G\) |
| \(10^{-9}\) | nano | \(n\) | \(10^{12}\) | tera | \(T\) |
| \(10^{-6}\) | micro | \(\mu\) | \(10^{15}\) | peta | \(P\) |
| \(10^{-3}\) | milli | \(m\) | \(10^{18}\) | exa | \(E\) |
| \(10^{-2}\) | centi | \(c\) | \(10^{21}\) | zetta | \(Z\) |
| \(10^{-1}\) | deci | \(d\) | \(10^{24}\) | yotta | \(Y\) |
Systems of Units
| Systems of Units | Length | Mass | Time | Force |
|---|---|---|---|---|
| cgs system | centimeter(cm) | gram(g) | second(s) | dyne |
| mks system | meter(m) | kilogram(kg) | second(s) | newton(N) |
| Engineering system | foot(ft) | slug | second(s) | pound(lb) |
SI-Unit : Fundamental Unit
| Quantity | symbol | Definition |
|---|---|---|
| Length | m | According to the current International Bureau of Weights and Measures (BIPM KCDB), 1m is the distance that light travels in a vacuum for 1/299792458 seconds, and 1 second is the time it takes for the light of a specific wavelength emitted from cesium-133 atoms to vibrate 9,192,631,770 times. |
| Mass | kg | Kilograms are units of mass. Kilogram is equal to the mass of the International Kilogram. |
| Time | s | The current international standard is the cesium atomic clock, which takes one second for the cesium-133 (133Cs) nucleus to vibrate 9,192,631,770 times. |
| Electric current | A | The SI unit of current is amperes, which means that 1 ampere flows 1 coulomb charge per second. One amperage is a constant current that flows in a vacuum in two straight conductors placed parallel to each other at 1 m intervals and exerts a force of 2 * 10 ^ (-7) N per meter of each of these conductors. |
| Temperature | K | The international unit of temperature is Kelvin (K). Kelvin is defined as 1 / 273.16 of the thermodynamic temperature of the triple point of water. By using the thermodynamic definition temperature in the temperature reference used in the general definition, even the temperature in the general definition can be related to the physical meaning and various fundamental physics. |
| Amount of subtance | mol | The quantity of matter is one of the basic quantities in the international system of units of quantity of substances such as atoms and molecules. In the international system of units, mole is defined as the unit of material quantity, and one mole corresponds to the amount of a substance of 12 grams (g) of carbon-12. |
| Luminous Intensity | cd | Candela (SI) is the SI unit of light intensity and means the luminous flux per unit solid angle of light emitted in a specific direction from a point light source. Candela is defined as the brightness when a light source emitting monochromatic light with a frequency of 540 × 1012 hertz radiates energy at a rate of 1/683 watts per steradian in any given direction. |
SI-Unit : Derived Unit
| Quantity | Symbol | Conversation |
|---|---|---|
| Frequency | \(Hz\) | \(1Hz=1s^{-1}\) |
| Electric charge | \(C\) | \(I=\frac{dQ}{dt}\) \(1C=1s\times 1A\) |
| Force | \(N\) | \(\overrightarrow { F }=m\overrightarrow { a }\) / \(\overrightarrow { a }=\frac { d^{ 2 }\overrightarrow { r } }{ dt^{ 2 } }\) \(1N=1kg\cdot 1m/s^{ 2 }\) |
| Angle | \(rad\) | \(\theta =\frac { r }{ l }\) 1rad is the center angle of the arc in which the radius r equals one circle and the arc length l equals one. |
| Solid angle | \(sr\) | \(\Omega =\frac { A }{ r^{ 2 } }\) 1 sr is the three-dimensional angle of the horn whose radius r is 1 and whose area A of a figure on the sphere is 1. |
| Luminous flux | \(lm\) | \(1 lm = 1cd\times 1sr\) |
| Illuminuance | \(lx\) | \(1lx=1cd/1m^{ 2 }\) |
| Energy | \(J\) | \(W=\int { \overrightarrow { F }\cdot d\overrightarrow { s } }\) / \(\overrightarrow { F }=m\overrightarrow { a }\) / \(\overrightarrow { a }=\frac { d^{ 2 }\overrightarrow { r } }{ dt^{ 2 } }\) \(\overrightarrow { F }=-\nabla U\) / \(\overrightarrow { F }=m\overrightarrow { a }\) / \(\overrightarrow { a }=\frac { d^{ 2 }\overrightarrow { r } }{ dt^{ 2 } }\) \(E=\frac { 1 }{ 2 }mv^{ 2 }\) / \(\overrightarrow { v }=\frac { d\overrightarrow { r } }{ dt }\) \(1 J = 1N \times 1m =1kg\cdot 1m/s^{ 2 }\cdot 1m=1kg\cdot m^{ 2 }/s^{ 2 }\) \(P=\frac { dE }{ dt }\) \(1 J = 1W \times 1s\) \(q\Delta V=\Delta U\) \(1 eV = 1.602177\times 10^{ -19 }J\) \(Ref]\ \Delta E=\sum { T }\) |
| Voltage | \(V\) | \(\Delta V=\frac { \Delta U }{ q }\) / \(W=\int { \overrightarrow { F }\cdot d\overrightarrow { s } }\) / \(\overrightarrow { F }=m\overrightarrow { a }\) / \(\overrightarrow { a }=\frac { d^{ 2 }\overrightarrow { r } }{ dt^{ 2 } }\) \(1 V = 1J/1C = 1kg\cdot m^{ 2 }/A\cdot s^{ 3 }\) \(\overrightarrow { E }=\frac { \overrightarrow { F } }{ q }=-\nabla V\) \(unit\ of\ electric\ field = 1N/1C = 1V/1m\) \(Ref]\ \overrightarrow { F }=q\overrightarrow { E }\) / \(\overrightarrow { E }=\frac { 1 }{ 4\pi \varepsilon _{ 0 } }\frac { Q }{ r^{ 3 } }\overrightarrow { r }\) / \(\oint _{ S }{ \overrightarrow { E }\cdot d\overrightarrow { a } }=\frac { Q }{ \varepsilon _{ 0 } }\) / \(\nabla \cdot \overrightarrow { E }=\frac { \rho }{ \varepsilon _{ 0 } }\) \(\oint _{ C }{ \overrightarrow { E }\cdot d\overrightarrow { l } }=-\frac { d }{ dt }\int _{ S }{ \overrightarrow { B }\cdot d\overrightarrow { a } }\) / \(\nabla \times \overrightarrow { E }=-\frac { \partial }{ \partial t }\overrightarrow { B }\) |
| Magnetic Field | \(T\) | \(\overrightarrow { F }=q\overrightarrow { v }\times \overrightarrow { B }\) / \(\overrightarrow { v }=\frac { d\overrightarrow { r } }{ dt }\) / \(I=\frac { dQ }{ dt }\) , \(\overrightarrow { F }=\int { I(d\overrightarrow { l }\times \overrightarrow { B }) }\) / \(I=\frac { dQ }{ dt }\) \(1 T =\frac { 1N }{ 1C\cdot 1m/s }=\frac { 1N }{ 1A\cdot 1m }\) \(1 T =10^{ 4 }G\) \(\Phi _{ B }=\int { \overrightarrow { B }\cdot d\overrightarrow { a } }\) \(1T = 1Wb/1m^{ 2 }\) \(Ref]\ \overrightarrow { F }=q\overrightarrow { v }\times \overrightarrow { B }\) / \(\overrightarrow { B }=\frac { \mu _{ 0 }I }{ 4\pi }\int { \frac { d\overrightarrow { l }\times (\overrightarrow { r }-\overrightarrow { r' }) }{ \left\vert \overrightarrow { r }-\overrightarrow { r' } \right\vert ^{ 3 } } }\) / \(\oint _{ S }^{ ' }{ \overrightarrow { B }\cdot d\overrightarrow { a } }=0\) \(\oint _{ C }{ \overrightarrow { B }\cdot d\overrightarrow { l } }=\mu _{ 0 }I+\mu _{ 0 }\varepsilon _{ 0 }\frac { d }{ dt }\int _{ S }{ \overrightarrow { E }\cdot d\overrightarrow { a } }\) / \(\nabla \times \overrightarrow { B }=\mu _{ 0 }\overrightarrow { J }+\mu _{ 0 }\varepsilon _{ 0 }\frac { \partial \overrightarrow { E } }{ \partial t }\) |
| Pressure | \(Pa\) | \(P=\frac { F }{ A }\) \(1T = 1Wb/1m^{ 2 }\) |
| Power | \(W\) | \(P=\frac { dE }{ dt }\) / \(W=\int { \overrightarrow { F }\cdot d\overrightarrow { s } }\) / \(\overrightarrow { F }=m\overrightarrow { a }\) / \(\overrightarrow { a }=\frac { d^{ 2 }\overrightarrow { r } }{ dt^{ 2 } }\) \(1 W = 1J/1s = 1kg\cdot m^{ 2 }/s^{ 3 }\) \(P=\frac { dE }{ dt }\) / \(\Delta V=\frac { \Delta U }{ q }\) / \(I=\frac { dQ }{ dt }\) \(1 W = 1A \times 1V\) |
| Electrical capacitance | \(F\) | \(Q=CV\) \(1F = 1C/1V\) |
| Electrical resistance | \(\Omega\) | \(V=IR\) , \(\overrightarrow { J }=\sigma \overrightarrow { E }\) / \(\overrightarrow { J }=\overrightarrow { I }/A\) / \(\overrightarrow { E }=-\nabla V\) \(1\Omega = 1V/1A\) |
| Electrical conductance | \(S\) | \(G=\frac { 1 }{ R }\) / \(V=IR\) \(1 Wb = 1T \times 1m^{ 2 }\) |
| Magnetic flux | \(Wb\) | \(\Phi _{ B }=\int { \overrightarrow { B }\cdot d\overrightarrow { a } }\) \(1 Wb = 1T \times 1m^{2}\) \(\Phi _{ B }=\int { \overrightarrow { B }\cdot d\overrightarrow { a } }\) / \(\oint _{ C }{ \overrightarrow { E }\cdot d\overrightarrow { l } }=-\frac { d }{ dt }\int _{ S }{ \overrightarrow { B }\cdot d\overrightarrow { a } }\) / \(\Delta V=-\int { \overrightarrow { E }\cdot d\overrightarrow { s } }\) , \(\Phi _{ B }=\int { \overrightarrow { B }\cdot d\overrightarrow { a } }\) / \(\nabla \times \overrightarrow { E }=-\frac { \partial }{ \partial t }\overrightarrow { B }\) / \(\Delta V=-\int { \overrightarrow { E }\cdot d\overrightarrow { s } }\) \(1 Wb = 1V \times 1s\) \(Ref]\ \oint _{ C }{ \overrightarrow { E }\cdot d\overrightarrow { l } }=-\frac { d }{ dt }\int _{ S }{ \overrightarrow { B }\cdot d\overrightarrow { a } }\) / \(\oint _{ S }^{ ' }{ \overrightarrow { B }\cdot d\overrightarrow { a } }=0\) / \(\nabla \cdot \overrightarrow { B }=0\) |
| Electrical inductance | \(H\) | \(\epsilon =-L\frac { dI }{ dt }\) / \(\epsilon =V\) / \(\Delta V=-\int { \overrightarrow { E }\cdot d\overrightarrow { s } }\) / \(\oint _{ C }{ \overrightarrow { E }\cdot d\overrightarrow { l } }=-\frac { d }{ dt }\int _{ S }{ \overrightarrow { B }\cdot d\overrightarrow { a } }\) \(1 H = 1V \times 1s/1A = 1Wb/1A\) |
Symbols, Dimensions, and Units of Physical Quantities
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Equations
| System | Equation |
|---|---|
| Classical Mechanics | \(\overrightarrow { a }=\frac { \overrightarrow { F } }{ m }\) |
| Classical Electromagnetics | \(\nabla \cdot \overrightarrow { E }=\frac { \rho }{ \varepsilon _{ 0 } }\) \(\nabla \times \overrightarrow { E }=-\frac { \partial \overrightarrow { B } }{ \partial t }\) \(\nabla \cdot \overrightarrow { B }=0\) \(\nabla \times \overrightarrow { B }=\mu _{ 0 }\overrightarrow { J }+\mu _{ 0 }\varepsilon _{ 0 }\frac { \partial \overrightarrow { E } }{ \partial t }\) \(\oint _{ S }{ \overrightarrow { E }\cdot d\overrightarrow { a }=\frac { Q }{ \varepsilon _{ 0 } } }\) \(\oint _{ C }{ \overrightarrow { E }\times d\overrightarrow { l }=-\frac { d }{ dt }\int _{ S }\overrightarrow { B }\cdot d\overrightarrow { a } }\) \(\oint _{ S }{ \overrightarrow { B }\cdot d\overrightarrow { a }=0 }\) \(\oint _{ C }{ \overrightarrow { B }\times d\overrightarrow { a }=\mu _{ 0 }\overrightarrow { I }+\mu _{ 0 }\varepsilon _{ 0 }\frac { d }{ dt }\int _{ S }\overrightarrow { E }\cdot d\overrightarrow { a } }\) \(\frac { \partial F^{ \mu \nu } }{ \partial x^{ \nu } }=\mu _{ 0 }J^{ \mu }\) \(\frac { \partial G^{ \mu \nu } }{ \partial x^{ \nu } }=0\) |
| Quantum System | \(i\hbar \frac { \partial }{ \partial t }\mid\Psi \rangle=\hat { H }\mid\Psi \rangle\) \(i\hbar \gamma ^{ \mu }\partial _{ \mu }\mid\Psi \rangle-mc\mid\Psi \rangle=0\) |
| Statistical and Thermal Physics | \(\Delta U=\sum { T }\) \(dS\ge 0\) |
| Optics | \(\frac { \partial ^{ 2 }u }{ \partial t^{ 2 } }=c^{ 2 }\nabla ^{ 2 }u\) |
| Solid State Physics | \(\psi (\overrightarrow { r })=e^{ i\overrightarrow { k }\cdot \overrightarrow { r } }u(\overrightarrow { r })\) |
| Fluid System | \(\frac { \partial u_{ i } }{ \partial t }+u_{ j }\frac { \partial u_{ i } }{ \partial x_{ j } }=f_{ i }-\frac { 1 }{ \rho }\frac { \partial p }{ \partial x_{ i } }+\nu \frac { \partial ^{ 2 }u_{ i } }{ \partial x_{ j }\partial x_{ j } }\) \(\frac { \partial \overrightarrow { u } }{ \partial t }+(\overrightarrow { u }\cdot \nabla )\overrightarrow { u }=\overrightarrow { f }-\frac { 1 }{ \rho }\nabla \overrightarrow { p }+\nu \nabla ^{ 2 }\overrightarrow { u }\) |
| General relativity | \(G_{ \mu \nu }+\Lambda _{ \mu \nu }=\frac { 8\pi G }{ c^{ 4 } }T_{ \mu \nu }\) |
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