Constants in Physics

Constants in Physics are fundamental values that remain unchanged across different contexts and experiments. These constants are universal in nature and are independent of the unit system used. They are essential for verifying the accuracy of theories and enabling practical applications based on those theories.

Some common constants are the Speed of Light in Vacuum (c), Planck’s Constant (h), Boltzmann Constant (k), Elementary Charge (e), etc. In this article, we will provide a comprehensive list of all important constants in physics.

What are Physical Constants?

Physical constants are fundamental quantities that cannot be explained by a theory and must be measured experimentally.

All physical constants are represented by some alphabet and have some value associated with them. The numerical values of dimensional physical constants depend on the unit system used to express them, but the physical constants themselves are independent of the unit system.

Universal Physical Constants

Some of the universal physical constants are:

• Speed of Light in Vacuum
• Planck Constant
• Gravitational Constant
• Boltzmann Constant
• Rydberg Constant

Speed of Light in Vacuum

Speed of Light in Vacuum is represented by “c” and has a value of 299,792.46 Km/sec. In other units, the speed of light is given as:

Units	Speed of Light in Vacuum
Meters per second (m/s)	299,792,458
Miles per second (mi/s)	186,282.397
Astronomical Units per day (AU/day)	173.1446
Light-years per year (ly/yr)	9.461×1012

Planck Constant

The Planck constant, symbolized as ‘h’, is a fundamental constant in physics, approximately equal to 6.626 x 10^-34 joule seconds (J·s). It describes the relationship between energy and frequency in quantum mechanics.

Gravitational Constant

The gravitational constant, denoted as ‘G’, has a value of approximately 6.674 × 10^-11 Newton meters squared per kilogram square (N.m²/kg²). It quantifies the strength of the gravitational force between two objects with mass.

Boltzmann Constant

The Boltzmann constant, represented by ‘k’, has a value of approximately 1.381 × 10^-23 joules per kelvin (J/K). The Boltzmann constant helps quantify the average energy per particle in a system at a given temperature.

Rydberg Constant

The Rydberg constant, denoted as ‘R_∞‘, is approximately equal to 1.097 × 10⁷ per meter (m^-1). The Rydberg constant relates to the wavelengths of spectral lines emitted or absorbed by these atoms.

Constant	Symbol	Value	Units
Speed of Light in Vacuum	c	299,792,458	meters per second (m/s)
Planck Constant	h	6.62607015×10−34	joule seconds (J⋅s)
Gravitational Constant	G	6.67430×10−11	cubic meters per kilogram per second squared (m3/kg/s2)
Boltzmann Constant	kB​	1.380649×10−23	joules per kelvin (J/K)
Rydberg Constant	R∞​	10,973,731.568527	per meter (1/m)

Some other universal physical constants are:

Constant	Symbol	Value	Units
Elementary Charge	e	1.602176634×10−19	coulombs (C)
Avogadro’s Number	NA​	6.022×1023	per mole
Permeability of Free Space	μ0​	4π×10−7	newton per ampere squared (N/A2)
Permittivity of Free Space	ε0​	8.854187817×10−12	farads per meter (F/m)
Fine-structure Constant	α	7.2973525693×10−3	dimensionless

Constants in Quantum Physics

In quantum mechanics, several fundamental constants play pivotal roles in describing the behaviour of particles at the smallest scales. These constants include Planck’s constant (h), the reduced Planck constant (ħ), the elementary charge (e), the electron rest mass (mₑ), and the speed of light in a vacuum (c).

As we’ve already discussed Planck’s Constant and Speed of light in vacuum, we’ll discuss the rest constants in quantum mechanics.

Constants	Symbol	Value	Units
Electron Rest Mass	mₑ	9.109 × 10-31	kilograms (kg)
Reduced Planck’s Constant	ħ	1.054 × 10-34	Joule Seconds (J·s)
Bohr Magneton	𝜇B	9.274 × 10-24	Joule per Tesla (J/T)

Reduced Planck Constant

The reduced Planck constant, denoted as ħ (pronounced “h-bar”), is a fundamental constant in quantum mechanics, defined as ħ = h / (2π), where h is Planck’s constant. Its value is approximately 1.054 × 10^-34 joule seconds (J·s).

Bohr Magneton

The Bohr magneton, denoted as μ_B, is a fundamental constant in quantum mechanics, approximately equal to 9.274 × 10^-24 joule per tesla (J/T). It represents the magnetic moment of an electron due to its orbital angular momentum in a hydrogen atom.

Electromagnetic Constants

In electromagnetism, several fundamental constants characterize the behavior of electric and magnetic fields. These constants include the permittivity of free space (ε₀), the permeability of free space (μ₀), and the speed of light in a vacuum (c).

Constant	Symbol	Value	Units
Permittivity of free space	ε₀	8.854 × 10-12	farads per meter (F/m)
Permeability of free space	μ₀	4π×10−7	Newton per Ampere squared (N/A2)

Gravitational and Cosmological Constants

Gravitational and cosmological constants are fundamental parameters in physics and cosmology that play crucial roles in understanding the structure, evolution, and behavior of the universe.

Constant	Symbol	Value	Units
Gravitational Constant	G	6.674 × 10-11	Newton meters squared per kilogram squared (N.m2/kg2)
Cosmological Constant	Λ	1.1056 × 10-52	Per square meter (1/m2)

Newtonian Constant of Gravitation

The terms “gravitational constant” and “Newtonian gravitational constant” are often used interchangeably to refer to the same fundamental constant, denoted as G.

Cosmological Constants

Cosmological constants, often denoted by Λ (lambda), are parameters that arise in cosmological models, such as the Lambda-CDM (Lambda cold dark matter) model, which describes the large-scale structure and evolution of the universe.

Thermodynamic Constants

Thermodynamic constants are fundamental parameters in thermodynamics, the branch of physics that deals with heat, energy, and work. These constants play essential roles in describing the behaviour of matter and energy in various physical systems, providing foundational principles for understanding and predicting thermodynamic processes.

Some of the key thermodynamic constants include:

• Gas Constant (R)
• Avogadro’s Number (N_A)
• Stefan-Boltzmann Constant (σ)

Let’s discuss these constant in detail.

Gas Constant (R)

This constant, denoted by R, represents the universal gas constant and is fundamental in the ideal gas law. Its value is 8.3145 in joules per mole per kelvin (J/mol/K) or in other appropriate units depending on the context.

Avogadro’s Number (NA)

Avogadro’s number, denoted by N_A, represents the number of atoms, molecules, or particles in one mole of a substance. Its value is approximately 6.022 × 10²³ per mole (mol^-1), and it plays a crucial role in converting between macroscopic and microscopic scales in thermodynamics.

Stefan-Boltzmann Constant (σ)

The Stefan-Boltzmann constant, denoted by σ, relates the total energy radiated by a blackbody to its temperature. It has a value of approximately 5.670 × 10^-8 watts per square meter per kelvin to the fourth power (W/m²/K⁴) and is essential for understanding radiative heat transfer in thermodynamic systems.

All the important constants in thermodynamics are listed in the following table:

Constants	Symbol	Value	Units
Gas Constant	R	8.3145	Joules per Mole per Kelvin (J/mol/K)
Avogadro Number	NA	6.022 × 1023	Per Mole (mol-1)
Stefan Boltzmann	σ	5.670 × 10-8	Watts per Square Meter per Kelvin to the fourth power (W/m2/K4)
Faraday Constant	F	96,485.33289	Coulombs per mole (L/mol)
Molar Volume of Ideal Gas at STP	Vm	22.414	Liters per Mole (L/mol)

Constants in Atomic and Nuclear Physics

Constants in atomic and nuclear physics are fundamental parameters that describe various aspects of atomic and nuclear systems. These constants play crucial roles in understanding the behavior of atoms, nuclei, and their interactions. Some important constants in atomic and nuclear physics include:

Constant	Symbol	Value	Units
Fine-Structure Constant	α	0.0072973525693	Dimensionless
Proton Rest Mass	mp​	1.6726219 × 10−27	Kilograms (kg)
Neutron Rest Mass	mn​	1.674927471 × 10−27	Kilograms (kg)
Proton-to-Electron Mass Ratio	mp/me	1836.15267389	Dimensionless
Bohr Radius	a0​	5.29177210903 × 10−11	Meters (m)
Unified Atomic Mass Unit (u)	u	1.66053906660 × 10−27	Kilograms (kg)
Nuclear Magneton	μN​	5.0507837461 × 10−27	Joules per tesla (J/T)

Conclusion

In summary, physical constants, dimensionless constants, and universal constants are foundational to physics, spanning quantum mechanics to nuclear physics. These constants, such as Planck’s constant and the speed of light, offer fixed numerical values crucial for understanding natural laws. They serve as fundamental pillars guiding theoretical models and experimental inquiries, illuminating the mysteries of the universe and driving scientific progress.

Physical Constant FAQs

What are Physical Constants?

Physical constants are fixed numerical values that are fundamental to various branches of physics.

How many physical constants are there in physics?

The number of physical constants in physics depends on the context and the level of detail considered.

What are Universal Physical Constants?

Universal physical constants are fundamental quantities in physics with fixed values, remaining constant across space and time.

Write examples of constants in Quantum Physics?

Examples of constants in quantum physics include Planck’s constant (h), the elementary charge (e), the fine-structure constant (α), and the Boltzmann constant (k).

What does c represent in physics?

In physics, c typically represents the speed of light in a vacuum.