Each measurement is a comparison of the measured quantity with another quantity that is homogeneous with it, which is considered to be unity. Theoretically, the units for all quantities in physics can be chosen to be independent of each other. But this is extremely inconvenient, since each value should have its own standard. In addition, in all physical equations that display the relationship between different quantities, there would be numerical coefficients.

The main feature of the currently used systems of units is that there are certain relationships between units of different quantities. These ratios are established by those physical laws (definitions) by which the measured values ​​are interconnected. Thus, the unit of speed is chosen in such a way that it is expressed in terms of units of distance and time. The speed units are used when selecting speed units. The unit of force, for example, is determined using Newton's second law.

When constructing a certain system of units, several physical quantities are chosen, the units of which are set independently of each other. Units of such quantities are called basic. The units of other quantities are expressed in terms of the basic ones, they are called derivatives.

Table of units of measure "Space and time"

Physical quantity	Symbol		Unit rev. physical led.	Description	Notes
	l, s, d			The length of an object in one dimension.
	S	square meter		The extent of an object in two dimensions.
Volume, capacity	V	cubic meter		The extent of an object in three dimensions.	extensive quantity
	t			Event duration.
flat corner	α , φ			The amount of change in direction.
Solid angle	α , β , γ	steradian		Part of space
Line speed	v	meters per second		The speed of changing body coordinates.
Linear acceleration	a, w	meters per second squared		The rate of change in the speed of an object.
Angular velocity	ω	radians per second	rad/s =	Angle change rate.
Angular acceleration	ε	radian per second squared	rad/s 2 =	Rate of change of angular velocity

Table of units of measurement "Mechanics"

Physical quantity	Symbol	Unit of measurement of a physical quantity	Unit rev. physical led.	Description	Notes
	m	kilogram		The value that determines the inertial and gravitational properties of bodies.	extensive quantity
Density	ρ	kilogram per cubic meter	kg / m 3	Mass per unit volume.	intense quantity
Surface density	ρ A	Mass per unit area.	kg/m2	The ratio of a body's mass to its surface area
Line Density	ρ l	Mass per unit length.		The ratio of body weight to its linear parameter
Specific volume	v	cubic meter per kilogram	m 3 /kg	The volume occupied by a unit mass of a substance
Mass flow	Qm	kilogram per second		The mass of matter that passes through given area flow cross section per unit time
Volume flow	Qv	cubic meter per second	m 3 / s	Volume flow of liquid or gas
	P	kilogram meter per second	kg m/s	The product of mass and velocity of a body.
angular momentum	L	kilogram meter squared per second	kg m 2 /s	A measure of the rotation of an object.	conserved quantity
	J	kilogram meter squared	kg m 2	A measure of the inertia of an object during rotation.	tensor quantity
Strength, weight	F, Q			The external cause of acceleration acting on the object.
Moment of power	M	newton meter	(kg m 2 / s 2)	The product of a force times the length of the perpendicular from a point to the line of action of the force.
Impulse of force	I	newton second		The product of a force and its duration
Pressure, mechanical stress	p , σ		Pa = ( kg / (m s 2))	Force per unit area.	intense quantity
	A		J= (kg m 2 / s 2)	The scalar product of force and displacement.
	E, U		J =(kg m 2 / s 2)	The ability of a body or system to do work.	extensive, conserved quantity, scalar
Power	N		W =(kg m 2 / s 3)	Rate of energy change.

Table of units of measurement "Periodic phenomena, oscillations and waves"

Physical quantity	Symbol	Unit of measurement of a physical quantity	Unit rev. physical led.	Description	Notes
	T			The time it takes for the system to make one complete oscillation
Batch Process Frequency	v, f			The number of repetitions of an event per unit of time.
Cyclic (circular) frequency	ω	radians per second	rad/s	Cyclic frequency electromagnetic oscillations in an oscillatory circuit.
Rotation frequency	n	second to the minus first power		A periodic process equal to the number of complete cycles completed per unit of time.
Wavelength	λ			The distance between two points in space closest to each other at which oscillations occur in the same phase.
wave number	k	meter to the minus first power		Spatial wave frequency

Units table " Thermal phenomena"

Physical quantity	Symbol	Unit of measurement of a physical quantity	Unit rev. physical led.	Description	Notes
Temperature	T			The average kinetic energy of the object's particles.	Intensive quantity
Temperature coefficient	α	kelvin to the minus first power		Dependence of electrical resistance on temperature
temperature gradient	gradT	kelvin per meter		Temperature change per unit length in the direction of heat propagation.
Heat (amount of heat)	Q		J =(kg m 2 / s 2)	Energy transferred from one body to another by non-mechanical means
Specific heat	q	joule per kilogram	j/kg	The amount of heat that must be applied to a substance at its melting point in order to melt it.
Heat capacity	C	joule per kelvin		The amount of heat absorbed (released) by the body in the process of heating.
Specific heat	c	joule per kilogram kelvin	J/(kg K)	The heat capacity of a unit mass of a substance.
Entropy	S	joule per kilogram	j/kg	A measure of the irreversible dissipation of energy or the uselessness of energy.

Units table " Molecular physics"

Physical quantity	Symbol	Unit of measurement of a physical quantity	Unit rev. physical led.	Description	Notes
Amount of substance	v, n		mole	The number of similar structural units that make up a substance.	Extensive quantity
Molar mass	M , μ	kilogram per mole	kg/mol	The ratio of the mass of a substance to the number of moles of that substance.
molar energy	H pier	joule per mole	J/mol	Energy of a thermodynamic system.
Molar heat capacity	with a pier	joule per mole kelvin	J/(mol K)	The heat capacity of one mole of a substance.
Molecule concentration	c, n	meter to the minus third power		The number of molecules contained in a unit volume.
Mass concentration	ρ	kilogram per cubic meter	kg / m 3	The ratio of the mass of a component contained in a mixture to the volume of the mixture.
Molar concentration	with a pier	moles per cubic meter	mol / m 3
Ion mobility	AT , μ	square meter per volt second	m 2 / (V s)	The coefficient of proportionality between the drift velocity of the carriers and the applied external electric field.

Units table " Electricity and magnetism"

Physical quantity	Symbol	Unit of measurement of a physical quantity	Unit rev. physical led.	Description	Notes
Current strength	I			Charge flowing per unit time.
current density	j	ampere per square meter		Strength electric current flowing through a surface element of unit area.	Vector quantity
Electric charge	Q, q		Cl =(A s)	The ability of bodies to be a source of electromagnetic fields and to take part in electromagnetic interaction.	extensive, conserved quantity
Electric dipole moment	p	coulomb meter		Electrical properties of a system of charged particles in terms of the field created by it and the action of external fields on it.
Polarization	P	pendant per square meter	C/m 2	Processes and states associated with the separation of any objects, mainly in space.
Voltage	U			The change in potential energy per unit of charge.
Potential, EMF	φ, σ			The work of external forces (non-Coulomb) to move the charge.
	E	volt per meter		The ratio of the force F acting on a fixed point charge placed in given point field, to the value of this charge q
Electrical capacitance	C			A measure of a conductor's ability to store an electrical charge
Electrical resistance	R, r		Ohm =(m 2 kg / (s 3 A 2))	resistance of an object to the passage of electric current
Specific electrical resistance	ρ			The ability of a material to block the passage of an electric current
electrical conductivity	G			The ability of a body (environment) to conduct electric current
Magnetic induction	B			Vector quantity, which is a force characteristic magnetic field	Vector quantity
magnetic flux	F		(kg/(s 2 A))	A value that takes into account the intensity of the magnetic field and the area it occupies.
Magnetic field strength	H	ampere per meter		The difference between the magnetic induction vector B and the magnetization vector M	Vector quantity
Magnetic moment	pm	ampere square meter		The value characterizing the magnetic properties of a substance
Magnetization	J	ampere per meter		The value characterizing the magnetic state of a macroscopic physical body.	vector quantity
Inductance	L			The coefficient of proportionality between the electric current flowing in any closed circuit and the total magnetic flux
electromagnetic energy	N		J =(kg m 2 / s 2)	Energy contained in an electromagnetic field
Bulk energy density	w	joule per cubic meter	J / m 3	Energy electric field capacitor
Active power	P			AC power
Reactive power	Q			The value characterizing the loads created in electrical devices by energy fluctuations electromagnetic field in AC circuit
Full power	S	watt-ampere		The total power, taking into account its active and reactive components, as well as the deviation of the current and voltage form from harmonic

Units table " Optics, electromagnetic radiation"

Physical quantity	Symbol	Unit of measurement of a physical quantity	Unit rev. physical led.	Description	Notes
The power of light	J, I			The amount of light energy emitted in a given direction per unit time.	Light, extensive quantity
Light flow	F			Physical quantity characterizing the amount of "light" power in the corresponding radiation flux
light energy	Q	lumen second		A physical quantity that characterizes the ability of the energy carried by light to cause visual sensations in a person.
illumination	E			The ratio of the luminous flux incident on a small surface area to its area.
Luminosity	M	lumens per square meter	lm/m2	A luminous quantity representing a luminous flux
	L, B	candela per square meter	cd/m2	The intensity of light emitted by a unit surface area in a particular direction
Radiation energy	E, W		J =(kg m 2 / s 2)	Energy carried by optical radiation

Table of units "Acoustics"

Physical quantity	Symbol	Unit of measurement of a physical quantity	Unit rev. physical led.	Description	Notes
Sound pressure	p			Variable overpressure arising in an elastic medium when a sound wave passes through it
Volumetric velocity	c, V	cubic meter per second	m 3 / s	The ratio of the volume of feedstock fed into the reactor per hour to the volume of catalyst
Sound speed	v, u	meters per second		Velocity of propagation of elastic waves in a medium
Sound intensity	l	watt per square meter	W/m2	The value characterizing the power transferred sound wave in the direction of propagation	scalar physical quantity
Acoustic impedance	Z a , R a	pascal second per cubic meter	Pa s / m 3	The ratio of the amplitude of sound pressure in a medium to the oscillatory velocity of its particles during the passage of a sound wave through the medium
Mechanical resistance	Rm	newton second per meter	N s/m	Indicates the force required to move the body at each frequency

Units table " Atomic and nuclear physics. Radioactivity"

Physical quantity	Symbol	Unit of measurement of a physical quantity	Unit rev. physical led.	Description	Notes
Mass (rest mass)	m	kilogram		The mass of an object at rest.
mass defect	Δ	kilogram		Quantity expressing the influence of internal interactions on the mass of a composite particle
elementary electric charge	e			Minimum portion (quantum) electric charge observed in nature for free long-lived particles
Bond energy	E St		J =(kg m 2 / s 2)	The difference between the energy of the state in which the constituent parts of the system are infinitely removed
Half-life, mean lifetime	T, t			The time during which the system decays in the approximate ratio 1/2
Effective cross section	σ	square meter		The value characterizing the probability of interaction of an elementary particle with atomic nucleus or another particle
Nuclide activity		becquerel		A value equal to the ratio total number decays of radioactive nuclei of the nuclide in the source by the time of decay
Energy of ionizing radiation	E,W		J =(kg m 2 / s 2)	The kind of energy released by atoms in the form electromagnetic waves(gamma or x-rays) or particles
Absorbed dose of ionizing radiation	D			The dose at which 1 joule of ionizing radiation energy is transferred to a mass of 1 kg
Equivalent dose of ionizing radiation	H , D eq			Absorbed dose of any ionizing radiation equal to 100 ergs per 1 gram of irradiated substance
Exposure dose of X-ray and gamma radiation	X	coulomb per kilogram	C/kg	the ratio of the total electric charge of ions of the same sign from external gamma radiation

Symbols in physics with multiple letters

Several letters or individual words or abbreviations are sometimes used to designate some quantities. So, constant often referred to in the formula as

Differential is indicated by a small letter

Before the value name, for example .

Special symbols

For the convenience of writing and reading among physicists, it is customary to use special symbols that characterize certain phenomena and properties.

In physics, it is customary to use not only formulas that are used in mathematics, but also specialized brackets.

Diacritics

Diacritical marks are added to the symbol for a physical quantity to indicate certain differences. Below, diacritics are added for example to the letter x.

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Building drawings is not an easy task, but without it in modern world no way. Indeed, in order to make even the most ordinary object (a tiny bolt or nut, a book shelf, the design of a new dress, and the like), you first need to carry out the appropriate calculations and draw a drawing of the future product. However, it is often made by one person, and another is engaged in the manufacture of something according to this scheme.

In order to avoid confusion in understanding the depicted object and its parameters, it is accepted all over the world conventions length, width, height and other quantities used in the design. What are they? Let's find out.

Quantities

Area, height and other designations of a similar nature are not only physical, but also mathematical quantities.

Their single letter designation (used by all countries) was established in the middle of the twentieth century by the International System of Units (SI) and is used to this day. It is for this reason that all such parameters are indicated in Latin, and not in Cyrillic letters or Arabic script. In order not to create separate difficulties, when developing design documentation standards in most modern countries, it was decided to use almost the same symbols that are used in physics or geometry.

Any school graduate remembers that depending on whether a two-dimensional or three-dimensional figure (product) is shown in the drawing, it has a set of basic parameters. If there are two dimensions - this is the width and length, if there are three - the height is also added.

So, for starters, let's find out how to correctly indicate the length, width, height in the drawings.

Width

As mentioned above, in mathematics, the quantity under consideration is one of the three spatial dimensions of any object, provided that its measurements are made in the transverse direction. So what is the famous width? It is designated with the letter "B". This is known all over the world. Moreover, according to GOST, the use of both capital and lowercase Latin letters is permissible. The question often arises as to why such a letter was chosen. After all, usually the reduction is made according to the first Greek or English name quantities. In this case, the width in English will look like "width".

Probably, the point here is that this parameter was originally most widely used in geometry. In this science, describing figures, often the length, width, height are denoted by the letters "a", "b", "c". According to this tradition, when choosing, the letter "B" (or "b") was borrowed by the SI system (although non-geometric symbols began to be used for the other two dimensions).

Most believe that this was done in order not to confuse the width (designated by the letter "B" / "b") with the weight. The fact is that the latter is sometimes referred to as "W" (short for the English name weight), although the use of other letters ("G" and "P") is also acceptable. According to the international standards of the SI system, the width is measured in meters or multiples (longitudinal) of their units. It is worth noting that in geometry it is sometimes also acceptable to use "w" to denote width, but in physics and other exact sciences this notation is generally not used.

Length

As already mentioned, in mathematics, length, height, width are three spatial dimensions. Moreover, if the width is a linear dimension in the transverse direction, then the length is in the longitudinal direction. Considering it as a quantity of physics, one can understand that this word means a numerical characteristic of the length of lines.

AT English language this term is called length. It is because of this that this value is indicated by the capital or lowercase initial letter of this word - “L”. Like width, length is measured in meters or their multiples (longitudinal) units.

Height

The presence of this value indicates that one has to deal with a more complex - three-dimensional space. Unlike length and width, height quantifies the size of an object in the vertical direction.

In English, it is written as "height". Therefore, according to international standards, it is designated by the Latin letter "H" / "h". In addition to the height, in the drawings, sometimes this letter also acts as a depth designation. Height, width and length - all of these parameters are measured in meters and their multiples and submultiples (kilometers, centimeters, millimeters, etc.).

Radius and Diameter

In addition to the parameters considered, when drawing up drawings, one has to deal with others.

For example, when working with circles, it becomes necessary to determine their radius. This is the name of a segment that connects two points. The first one is the center. The second is located directly on the circle itself. In Latin, this word looks like "radius". Hence the lowercase or capital "R"/"r".

When drawing circles, in addition to the radius, one often has to deal with a phenomenon close to it - the diameter. It is also a line segment connecting two points on a circle. However, it must pass through the center.

Numerically, the diameter is equal to two radii. In English, this word is written like this: "diameter". Hence the abbreviation - a large or small Latin letter "D" / "d". Often the diameter in the drawings is indicated with a crossed out circle - “Ø”.

Although this is a common abbreviation, it should be borne in mind that GOST provides for the use of only the Latin "D" / "d".

Thickness

Most of us remember school lessons mathematics. Even then, teachers said that it was customary to designate such a quantity as area with the Latin letter “s”. However, according to generally accepted standards, a completely different parameter is recorded in the drawings in this way - thickness.

Why is that? It is known that in the case of height, width, length, the designation with letters could be explained by their spelling or tradition. That's just the thickness in English looks like "thickness", and in the Latin version - "crassities". It is also not clear why, unlike other quantities, the thickness can be denoted only by a lowercase letter. The "s" designation is also used to describe the thickness of pages, walls, ribs, and so on.

Perimeter and area

Unlike all the quantities listed above, the word "perimeter" did not come from Latin or English, but from Greek. It is derived from "περιμετρέο" ("to measure the circumference"). And today this term has retained its meaning (the total length of the borders of the figure). Subsequently, the word got into the English language ("perimeter") and was fixed in the SI system in the form of an abbreviation with the letter "P".

Area is a quantity showing a quantitative characteristic geometric figure, which has two dimensions (length and width). Unlike everything listed above, it is measured in square meters(as well as in submultiples and multiples of their units). As for the letter designation of the area, then in different areas it is different. For example, in mathematics, this is the Latin letter “S”, familiar to everyone since childhood. Why so - there is no information.

Some people unknowingly think that this is due to English spelling the words "square". However, in it the mathematical area is "area", and "square" is the area in the architectural sense. By the way, it is worth remembering that "square" is the name of the geometric figure "square". So you should be careful when studying drawings in English. Due to the translation of "area" in some disciplines, the letter "A" is used as a designation. In rare cases, "F" is also used, but in physics this letter means a quantity called "force" ("fortis").

Other common abbreviations

The designations of height, width, length, thickness, radius, diameter are the most used in drawing up drawings. However, there are other quantities that are also often present in them. For example, lowercase "t". In physics, this means "temperature", however, according to the GOST of the Unified System for Design Documentation, this letter is a pitch (of helical springs, and the like). However, it is not used when it comes to gears and threads.

Capital and lowercase letter"A" / "a" (according to all the same standards) in the drawings is used to indicate not the area, but the center-to-center and center-to-center distance. In addition to various values, in the drawings it is often necessary to designate angles of different sizes. For this, it is customary to use lowercase letters of the Greek alphabet. The most used are "α", "β", "γ" and "δ". However, others can be used as well.

What standard defines the letter designation of length, width, height, area and other quantities?

As mentioned above, so that there is no misunderstanding when reading the drawing, representatives of different peoples accepted common standards letter designation. In other words, if you are in doubt about the interpretation of a particular abbreviation, look at GOSTs. Thus, you will learn how to correctly indicate the height, width, length, diameter, radius, and so on.

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Books

• Hydraulics. Textbook and workshop for academic bachelor's degree, Kudinov V.A.
• Hydraulics 4th ed., trans. and additional Textbook and workshop for academic baccalaureate, Eduard Mikhailovich Kartashov. The textbook outlines the basic physical and mechanical properties of liquids, issues of hydrostatics and hydrodynamics, gives the basics of the theory of hydrodynamic similarity and mathematical modeling ...

Cheat sheet with formulas in physics for the exam

and not only (may need 7, 8, 9, 10 and 11 classes).

For starters, a picture that can be printed in a compact form.

Mechanics

1. Pressure P=F/S
2. Density ρ=m/V
3. Pressure at the depth of the liquid P=ρ∙g∙h
4. Gravity Ft=mg
5. 5. Archimedean force Fa=ρ w ∙g∙Vt
6. The equation of motion for uniformly accelerated motion

X=X0 + υ 0∙t+(a∙t 2)/2 S=( υ 2 -υ 0 2) /2а S=( υ +υ 0) ∙t /2

1. Velocity equation for uniformly accelerated motion υ =υ 0 +a∙t
2. Acceleration a=( υ -υ 0)/t
3. Circular speed υ =2πR/T
4. Centripetal acceleration a= υ 2/R
5. Relationship between period and frequency ν=1/T=ω/2π
6. Newton's II law F=ma
7. Hooke's law Fy=-kx
8. Law of universal gravitation F=G∙M∙m/R 2
9. The weight of a body moving with acceleration a P \u003d m (g + a)
10. The weight of a body moving with acceleration a ↓ P \u003d m (g-a)
11. Friction force Ffr=µN
12. Body momentum p=m υ
13. Force impulse Ft=∆p
14. Moment M=F∙ℓ
15. Potential energy of a body raised above the ground Ep=mgh
16. Potential energy of elastically deformed body Ep=kx 2 /2
17. Kinetic energy of the body Ek=m υ 2 /2
18. Work A=F∙S∙cosα
19. Power N=A/t=F∙ υ
20. Efficiency η=Ap/Az
21. Oscillation period of the mathematical pendulum T=2π√ℓ/g
22. Oscillation period of a spring pendulum T=2 π √m/k
23. The equation harmonic vibrationsХ=Хmax∙cos ωt
24. Relationship of the wavelength, its speed and period λ= υ T

Molecular physics and thermodynamics

1. Amount of substance ν=N/ Na
2. Molar mass M=m/ν
3. Wed. kin. energy of monatomic gas molecules Ek=3/2∙kT
4. Basic equation of MKT P=nkT=1/3nm 0 υ 2
5. Gay-Lussac law (isobaric process) V/T =const
6. Charles' law (isochoric process) P/T =const
7. Relative humidity φ=P/P 0 ∙100%
8. Int. ideal energy. monatomic gas U=3/2∙M/µ∙RT
9. Gas work A=P∙ΔV
10. Boyle's law - Mariotte (isothermal process) PV=const
11. The amount of heat during heating Q \u003d Cm (T 2 -T 1)
12. The amount of heat during melting Q=λm
13. The amount of heat during vaporization Q=Lm
14. The amount of heat during fuel combustion Q=qm
15. The equation of state for an ideal gas is PV=m/M∙RT
16. First law of thermodynamics ΔU=A+Q
17. Efficiency of heat engines η= (Q 1 - Q 2) / Q 1
18. Ideal efficiency. engines (Carnot cycle) η \u003d (T 1 - T 2) / T 1

Electrostatics and electrodynamics - formulas in physics

1. Coulomb's law F=k∙q 1 ∙q 2 /R 2
2. Electric field strength E=F/q
3. Email tension. fields point charge E=k∙q/R2
4. Surface charge density σ = q/S
5. Email tension. fields of the infinite plane E=2πkσ
6. Dielectric constant ε=E 0 /E
7. Potential energy of interaction. charges W= k∙q 1 q 2 /R
8. Potential φ=W/q
9. Point charge potential φ=k∙q/R
10. Voltage U=A/q
11. For a uniform electric field U=E∙d
12. Electric capacity C=q/U
13. Capacitance of a flat capacitor C=S∙ ε ∙ε 0/d
14. Energy of a charged capacitor W=qU/2=q²/2С=CU²/2
15. Current I=q/t
16. Conductor resistance R=ρ∙ℓ/S
17. Ohm's law for the circuit section I=U/R
18. The laws of the last compounds I 1 \u003d I 2 \u003d I, U 1 + U 2 \u003d U, R 1 + R 2 \u003d R
19. Parallel laws. conn. U 1 \u003d U 2 \u003d U, I 1 + I 2 \u003d I, 1 / R 1 + 1 / R 2 \u003d 1 / R
20. Electric current power P=I∙U
21. Joule-Lenz law Q=I 2 Rt
22. Ohm's law for a complete chain I=ε/(R+r)
23. Short circuit current (R=0) I=ε/r
24. Magnetic induction vector B=Fmax/ℓ∙I
25. Ampere Force Fa=IBℓsin α
26. Lorentz force Fл=Bqυsin α
27. Magnetic flux Ф=BSсos α Ф=LI
28. Law of electromagnetic induction Ei=ΔФ/Δt
29. EMF of induction in moving conductor Ei=Вℓ υ sinα
30. EMF of self-induction Esi=-L∙ΔI/Δt
31. The energy of the magnetic field of the coil Wm \u003d LI 2 / 2
32. Oscillation period count. contour T=2π ∙√LC
33. Inductive reactance X L =ωL=2πLν
34. Capacitance Xc=1/ωC
35. The current value of the current Id \u003d Imax / √2,
36. RMS voltage Ud=Umax/√2
37. Impedance Z=√(Xc-X L) 2 +R 2

Optics

1. The law of refraction of light n 21 \u003d n 2 / n 1 \u003d υ 1 / υ 2
2. Refractive index n 21 =sin α/sin γ
3. Thin lens formula 1/F=1/d + 1/f
4. Optical power of the lens D=1/F
5. max interference: Δd=kλ,
6. min interference: Δd=(2k+1)λ/2
7. Differential grating d∙sin φ=k λ

The quantum physics

1. Einstein's formula for the photoelectric effect hν=Aout+Ek, Ek=U ze
2. Red border of the photoelectric effect ν to = Aout/h
3. Photon momentum P=mc=h/ λ=E/s

Physics of the atomic nucleus

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