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Physics

Constants in Physics

Constants in Physics

Q: 2. What is the difference between a fundamental constant and a derived quantity?

A fundamental constant is a basic quantity believed to be universal and unchanging, like Planck's constant (h). A derived quantity, in contrast, is defined in terms of other physical quantities and can vary. For example, velocity is a derived quantity (distance divided by time) and changes with an object's motion, whereas the speed of light in a vacuum (c) is a constant.

Q: 7. What is the magnetic constant (μ₀) and where is it applied in physics?

The magnetic constant, also known as the permeability of free space and symbolised by μ₀, is a physical constant that describes the ability of a vacuum to support a magnetic field. Its defined value is exactly 4π × 10⁻⁷ H/m. It is a key component in Ampere's Law and other equations in electromagnetism, connecting electric currents to the magnetic fields they create.

Reviewed by:

Gaurang Shah

What are Constants in Physics?

The significance of constants in Physics is that throughout all of the formulations of the basic theories of Physics and the application to the real world, physical constants appear as fundamental invariant quantities, and they have specific and universally used symbols, that are of such importance that they must be known to as high an accuracy as is possible.

The physical constant also called the fundamental constant or the universal constant is a physical quantity that is believed to be universal in nature and has a constant value at all times.

Fundamental Constants in Physics

Speed of light in vacuum = c

Planck’s constant = h

The electric constant = ε0

The elementary charge = e

Constant Value in Physics

In physics, we deal with various dimensions, and to set the dimensions of an entity, the time length of an event, or the density of the fluid we need to compare them with other entities, we use as a reference. These entities are the constants of physics, such as the speed of light (c), the charge of the electron(e) or mass (mp) of a proton, Rydberg constant, and so on.

For example, the value of Avogadro's number is 6.02214 x 10²³ mol⁻¹ remains the same everywhere.

Important Physical Constants

There are various fundamental constants to describe the universe as completely as possible; a few are listed below:

Table: List of All Constants in Physics

S.No	Name	Formula	Value
1.	Von Klitzing constant	Rk = 2πh/e²	25812.80745...Ω
2.	Curie constant	C = X (T - θ)	1.3047 K * A/(T * m)
3.	Fine-structure constant	α = e²/2hcε0	0.007297351
4.	Compton wavelength	λ = h/mc	In meter: 2.42 x 10⁻¹²m In Angstrom = 0.242 Å
5.	Impedance of free space	Z0 = 1/ε0c0	376.730...Ω
6.	Bohr radius	a0 = 4πε0 h²/e²mₑ	0.0529 m
7.	Faraday constant	F = eNA	96,485 C/mol
8.	Vacuum electric permittivity	ε0 = 1/μ0c²	8.854 x 10⁻¹² F.m
9.	Stefan–Boltzmann constant	σ = π²k⁴/60h³c²	5.67 x 10⁻⁸Js⁻¹m⁻²K⁻⁴
10.	Thomson cross section	σe = (8π/3)re²	6.6524587321 x 10⁻²⁹ m²
11.	Vacuum magnetic permeability	μ0	1.25663706212(19)x10⁻⁶N. A⁻²

All physics constants

Table: All Constant Values in Physics

S.No.	Name	Symbol	Formula	Value
1.	Reduced Planck constant	ħ	h/2π	1.05457 x 10⁻³⁴ J.s
2.	Deuteron mass	mD	--	2.013553212745(40) u 1875.612928(12)MeV 1.67377 x 10⁻²⁷ kg or 1.67377 x 10⁻²⁴g
3.	Josephson constant	KJ	2e/h	483597.84... x 10⁸ Hz./V
4.	Rydberg constant	R∞	α². mec/2h	10.973731.56(12)m⁻¹
5.	Proton mass	mp	--	1.672621898(21) x 10⁻²⁷ kg 1.672621898(21) x 10⁻²⁴ kg 1.007276466879(91)u 938.2720813(58) MeV/c²
6.	Neutron mass	mn	--	1.674927471(21) x 10⁻²⁷ kg 1.674927471(21) x 10⁻²⁴ g 1.00866491588(49) u 939.5654133(58) MeV/c²
7.	Electron mass	me	--	9.10938356(11) x 10⁻³¹ kg 9.10938356(11) x 10⁻²⁸ g 5.48579909070(16) amu 0.5109989461(31)MeV/c²
8.	Boltzmann’s constant	Kb		1.380649 x 10⁻²³ J/K 1.380649 x 10⁻¹⁶erg/K
9.	Rest mass of the electron	me	2R∞h/cα²	0.51099895000(15) Mev
11.	Gas constant	R	--	8.3144598(48) J/K mol 8.3144598(48) x 10³ amu.m²/s²K 8.3144598(48) x 10⁻² L.bar/K mol 8.3144598(48) m³ .Pa/K.mol 62.363577(36) L.T or/K.mol 1.9872036(11) x 10⁻³ Kcal/K.mol 8.2057338(47)x10⁻⁵m³.atm/K.mol 0.082057338(47) L.atm/K.mol
12.	Alpha particle mass	mα	--	6.644657230(82) x ⁻²⁷ kg 4.001506179127(63) u 3.727379378(23) GeV/c²

Famous Constants in Physics

There are so many constants besides those I mentioned above, but some constants in physics are recognized widely.

Constant values in physics that are most popular among all the physical constants are as follows:

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S.No.	Name	Symbol	Value
1.	Speed of the light in vacuum	c	3 x 10⁸ m/s
2.	Planck’s constant	h	6.62607015 x 10⁻³⁴ J.s
3.	Gravitational constant	G	6.673 x 10⁻¹¹ Nm²/kg²
4.	Elementary charge	e, qe (charge of a proton)	1.602176634 x 10⁻¹⁹ C
5.	Electric constant	ε0	8.9875517923(14) x 10⁹ kg.m³.s⁻⁴.A⁻²

The physical constant is a complex concept that is taught in class 11 physics. This is based on the curriculum set by the Central Board of secondary education and physical constants or Constance of Physics holds a significant weightage in the examination and therefore are extremely important to understand. The concept of physical constants can be studied in depth in the study notes that I provided by Vedanta, these notes are repaired by Vedanta’s export research team who are well-versed in research and curating study notes for students, Vedantu’s exports have extensive experience and have done thorough research in the duration of these study notes. The notes provided by Vedanta are based on the latest CBSE curriculum and are therefore up to date.

Physical constants are known by different titles such as fundamental constant, universal constant, Constance of physics. It is extremely important to have an accurate evaluation of the physical constants as their accuracy will help to check how up to the mark the theories are, as they form the basis of Physics their accuracy allows useful applications that can be made based on certain theories.

Physical constants are a set of fundamental quantities that appear in the basic theoretical equations of physics.

For example, a universal constant of nature is the speed of light in a vacuum (c). The speed of light can be studied in both electromagnetic theory and in relativity theory; in relativity theory, it relies on energy to Mass whose equation can be written as E =mc². The value of the speed of light never changes and it does not depend on any experimental conditions like the speed of a sound wave changes in some cases therefore, the speed of light is a universal constant

Table Representing Some Important Physical Constants

Quantity	Symbol	Value
constant of gravitation	G	6.67384 × 10−11 cubic meter per second squared per kilogram
speed of light (in a vacuum)	c	2.99792458 × 108 meters per second
Planck's constant	h	6.626070040 × 10−34 joule second
Boltzmann constant	k	1.38064852 × 10−23 joule per kelvin
Faraday constant	F	9.648533289 × 104 coulombs per mole
electron rest mass	me	9.10938356 × 10−31 kilogram
proton rest mass	mp	1.672621898 × 10−27 kilogram
neutron rest mass	mn	1.674927471 × 10−27 kilogram
charge on electron	e	1.6021766208 × 10−19 coulomb
Rydberg constant	R∞	1.0973731568508 × 107 per metre
Stefan-Boltzmann constant	σ	5.670367 × 10−8 watt per square meter per kelvin
fine-structure constant	α	7.2973525664 × 10−3

FAQs on Constants in Physics

1. What are physical constants and why are they important in physics?

A physical constant is a quantity in nature that has a universal, unchanging value. Examples include the speed of light (c) and the elementary charge (e). Their importance lies in their role as the foundation of physical theories; they connect different physical quantities in fundamental equations (like E=mc²) and allow for the verification of these theories through precise measurements, as per the CBSE 2025-26 syllabus.

2. What is the difference between a fundamental constant and a derived quantity?

A fundamental constant is a basic quantity believed to be universal and unchanging, like Planck's constant (h). A derived quantity, in contrast, is defined in terms of other physical quantities and can vary. For example, velocity is a derived quantity (distance divided by time) and changes with an object's motion, whereas the speed of light in a vacuum (c) is a constant.

3. What are some examples of fundamental constants used in the Class 11 & 12 NCERT syllabus?

Several key constants are crucial for the CBSE Class 11 and 12 Physics syllabus. Key examples include:

Speed of light in vacuum (c): ~3 x 10⁸ m/s. Used in Electromagnetism and Modern Physics.
Planck's constant (h): 6.626 x 10⁻³⁴ J·s. Fundamental to Quantum Mechanics.
Gravitational constant (G): 6.674 × 10⁻¹¹ N·m²/kg². Used in the Law of Universal Gravitation.
Elementary charge (e): 1.602 x 10⁻¹⁹ C. The charge of a single proton.
Permittivity of free space (ε₀): 8.854 x 10⁻¹² F/m. Used in Electrostatics.

4. Are all physical constants dimensionless? Explain with an example.

No, most physical constants have dimensions and units. For example, the speed of light (c) has dimensions of [L T⁻¹] and units of m/s. However, some constants are dimensionless, meaning they are pure numbers. A key example is the fine-structure constant (α), which has a value of approximately 1/137 and has no units. It describes the strength of the electromagnetic interaction.

5. What is the significance of the fine-structure constant, often cited as ~1/137?

The fine-structure constant, symbolised by alpha (α), is a fundamental dimensionless physical constant. Its significance is immense because it characterises the strength of the electromagnetic force that governs how electrically charged particles (like electrons) and photons interact. Its value, approximately 1/137, is independent of the system of units used, making it a truly universal measure of this core interaction in nature.

6. How are physical constants used to define standard units like the metre and second?

Modern metrology defines standard units based on the exact values of physical constants, ensuring their stability and universality. For example:

The metre is defined by taking the fixed numerical value of the speed of light in a vacuum (c) to be 299,792,458 when expressed in the unit m/s.
The second is defined based on the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom.

This approach makes our fundamental units independent of physical artefacts and universally reproducible.

7. What is the magnetic constant (μ₀) and where is it applied in physics?

The magnetic constant, also known as the permeability of free space and symbolised by μ₀, is a physical constant that describes the ability of a vacuum to support a magnetic field. Its defined value is exactly 4π × 10⁻⁷ H/m. It is a key component in Ampere's Law and other equations in electromagnetism, connecting electric currents to the magnetic fields they create.