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The 12 Important Physical Constants

Table of contents

The physical constants of physics are important for understanding the universe. The constants of nature are, as the name suggests, universal and unchanging values that are determined experimentally. Their values apply everywhere in the universe, so we can also infer the physics outside our Earth, outside our solar system and even the physics in other galaxies in our universe. In this lesson, we take a look at some of the most important natural constants and their significance for physics.

Speed of light

Speed of light tells us how fast light travels in empty space (vacuum).

$$ \begin{align} c ~=~ 299 \, 792 \, 458 \, \frac{\mathrm m}{ \mathrm s} \end{align} $$

This constant is the maximum speed at which information or signals can travel through space and plays a fundamental role in Albert Einstein's theory of relativity. The speed of light can be determined and its constancy confirmed using interferometer experiments (e.g. the Michaelson-Morley experiment).

Elementary charge

The elementary charge is the smallest, freely existing electric charge in our universe.

$$ \begin{align} e ~=~ 1.602 \, 176 \, 634 ~\cdot~ 10^{-19} \, \mathrm{C} \end{align} $$

All other electrically charged bodies carry a multiple of the elementary charge $e$. In our universe, the elementary charge determines how strongly elementary particles attract and repel each other. The value of the elementary charge can be determined using the Millikan experiment, for example.

Vacuum permeability

The vacuum permeability appears in equations that deal with magnetic fields.

$$ \begin{align} \mu_0 ~\approx~ 1.256 \, 637 \, 062 ~\cdot~ 10^{-6} \, \frac{\mathrm{Vs}}{\mathrm{Am}} \end{align} $$

The vacuum permeability combines magnetic flux density and magnetic field strength and influences phenomena such as electromagnetic induction.

Vacuum permittivity

The vacuum permittivity occurs in equations that deal with electric fields.

$$ \begin{align} \varepsilon_0 ~\approx~ 8.854 \, 187 \, 8128 ~\cdot~ 10^{-12} \, \frac{\mathrm{As}}{\mathrm{Vm}} \end{align} $$

Planck's constant

The Planck's constant, is a physical constant that appears in equations whenever the equation describes quantum effects.

$$ \begin{align} h ~=~ 6.626 \, 070 \, 15 ~\cdot~ 10^{-34} \, \mathrm{Js} \end{align} $$

Planck's constant describes the smallest possible action (in Joule seconds) of the universe in a physical process.

Gravitational constant

The gravitational constant occurs in Newton's law of gravity and Einstein field equations, which describe the interaction between masses.

$$ \begin{align} G ~\approx~ 6.674 \, 30 ~\cdot~ 10^{-11} \, \frac{ \mathrm{m}^3 }{ \mathrm{kg} \, \mathrm{s}^2 } \end{align} $$

The exact determination of the gravitational constant is crucial for the precision of astronomical calculations and the understanding of mass distributions in the universe.

Boltzmann constant

The Boltzmann constant occurs in equations which describe systems with many particles.

$$ \begin{align} k_{\text B} ~=~ 1.380 \, 649 ~\cdot~ 10^{-23} \, \frac{\mathrm{J}}{\mathrm{K}} \end{align} $$

The Boltzmann constant combines statistical mechanics with thermodynamics. It occurs, for example, in the Boltzmann distribution and indicates how the energy of particles is distributed over different energy levels. The Boltzmann constant is crucial for the definition of temperature.

Electron mass

The mass of one electron

$$ \begin{align} \class{brown}{m_{\text e}} ~\approx~ 9.109 \, 383 \, 701 \, 5 ~\cdot~ 10^{-32} \, \mathrm{kg} \end{align} $$

Proton mass

Mass of one proton

$$ \begin{align} \class{brown}{m_{\text p}} ~\approx~ 1.672 \, 621 \, 923 \, 69 ~\cdot~ 10^{-27} \, \mathrm{kg} \end{align} $$

Neutron mass

Mass of one neutron

$$ \begin{align} \class{brown}{m_{\text n}} ~\approx~ 1.674 \, 927 \, 498 \, 04 ~\cdot~ 10^{-27} \, \mathrm{kg} \end{align} $$

Avogadro constant

The Avogadro constant indicates how many particles are present in one mole.

$$ \begin{align} N_{\text A} ~=~ 6.022 \, 140 \, 76 \cdot 10^{23} \, \frac{1}{\mathrm{mol}} \end{align} $$

This constant is used, for example, to link the macroscopic and microscopic properties of matter. In the case of a gas, the Avogadro constant represents the link between volume, pressure and temperature.

Gas constant

The (universal) gas constant occurs in thermodynamics - in the description of gases (e.g. air).

$$ \begin{align} R ~=~ 8.314 \, 462 \, 618 \, 153 \, 24 \, \frac{\mathrm{J}}{ \mathrm{K} \, \mathrm{mol} } \end{align} $$

The gas constant occurs, for example, in the ideal gas law, which applies to ideal gases and describes the relationship between gas pressure, its volume, its temperature and the number of gas particles.