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| Boilerpipe Text | Top Questions
What is Brownian motion?
Who discovered Brownian motion and how?
What causes Brownian motion to happen?
How can we observe Brownian motion in everyday life?
Why was the explanation of Brownian motion important for science?
How does Brownian motion support the idea that atoms and molecules exist?
Brownian motion
, any of various physical phenomena in which some quantity is constantly undergoing small, random fluctuations. It was named for the Scottish botanist
Robert Brown
, the first to study such fluctuations (1827).
If a number of particles subject to Brownian motion are present in a given medium and there is no preferred direction for the random oscillations, then over a period of time the particles will tend to be spread evenly throughout the medium. Thus, if
A
and
B
are two
adjacent
regions and, at time
t
,
A
contains twice as many particles as
B
, at that instant the probability of a particle’s leaving
A
to enter
B
is twice as great as the probability that a particle will leave
B
to enter
A
. The physical process in which a substance tends to spread steadily from regions of high concentration to regions of lower concentration is called
diffusion
.
Diffusion
can therefore be considered a macroscopic
manifestation
of Brownian
motion
on the microscopic level. Thus, it is possible to study diffusion by simulating the motion of a Brownian particle and computing its average behaviour. A few examples of the countless diffusion processes that are studied in terms of Brownian motion include the diffusion of pollutants through the
atmosphere
, the diffusion of “holes” (minute regions in which the
electrical charge
potential is positive) through a
semiconductor
, and the diffusion of calcium through bone tissue in living organisms.
Early investigations
The term “classical Brownian motion” describes the random movement of microscopic particles suspended in a
liquid
or
gas
. Brown was investigating the fertilization process in
Clarkia pulchella
, then a newly discovered species of
flowering plant
, when he noticed a “rapid oscillatory motion” of the microscopic particles within the
pollen
grains suspended in water under the
microscope
. Other researchers had noticed this phenomenon earlier, but Brown was the first to study it. Initially he believed that such motion was a
vital
activity peculiar to the male sex cells of plants, but he then checked to see if the pollen of plants dead for over a century showed the same movement. Brown called this a “very unexpected fact of seeming vitality being retained by these ‘molecules’ so long after the death of the plant.” Further study revealed that the same motion could be observed not only with particles of other organic substances but even with chips of glass or granite and particles of smoke. Finally, in inarguable support of the nonliving nature of the phenomenon, he demonstrated it in fluid-filled vesicles in rock from the
Great Sphinx
.
Britannica Quiz
Physics and Natural Law
Early explanations
attributed
the motion to thermal
convection
currents in the
fluid
. When observation showed that nearby particles exhibited totally uncorrelated activity, however, this simple explanation was abandoned. By the 1860s theoretical physicists had become interested in Brownian motion and were searching for a consistent explanation of its various characteristics: a given particle appeared equally likely to move in any direction; further motion seemed totally unrelated to past motion; and the motion never stopped. An experiment (1865) in which a suspension was sealed in glass for a year showed that the Brownian motion persisted. More
systematic
investigation in 1889 determined that small particle size and low viscosity of the surrounding fluid resulted in faster motion.
Einstein
’s theory of Brownian motion
Since higher temperatures also led to more-rapid Brownian motion, in 1877 it was suggested that its cause lay in the “thermal molecular motion in the liquid environment.” The idea that molecules of a liquid or gas are constantly in motion, colliding with each other and bouncing back and forth, is a prominent part of the
kinetic theory of gases
developed in the third quarter of the 19th century by the physicists
James Clerk Maxwell
,
Ludwig Boltzmann
, and
Rudolf Clausius
in explanation of heat phenomena. According to the theory, the
temperature
of a substance is proportional to the average
kinetic energy
with which the molecules of the substance are moving or vibrating. It was natural to guess that somehow this motion might be imparted to larger particles that could be observed under the microscope; if true, this would be the first directly observable effect that would
corroborate
the kinetic theory. This line of reasoning led the German physicist
Albert Einstein
in 1905 to produce his quantitative theory of Brownian motion. Similar studies were carried out on Brownian motion, independently and almost at the same time, by the Polish physicist Marian Smoluchowski, who used methods somewhat different from Einstein’s.
Learn about Albert Einstein's theory of Brownian motion and how he derived the size of atoms based on how much the Brownian particles move
Description of Albert Einstein's theory of Brownian motion and how he derived the size of atoms.
See all videos for this article
Einstein wrote later that his major aim was to find facts that would guarantee as much as possible the existence of
atoms
of definite size. In the midst of this work, he discovered that according to
atomic theory
there would have to be an observable movement of suspended microscopic particles. Einstein did not realize that observations concerning the Brownian motion were already long familiar. Reasoning on the basis of
statistical mechanics
, he showed that for such a microscopic particle the random difference between the pressure of molecular bombardment on two opposite sides would cause it to constantly
wobble
back and forth. A smaller particle, a less viscous fluid, and a higher temperature would each increase the amount of motion one could expect to observe. Over a period of time, the particle would tend to drift from its starting point, and, on the basis of kinetic theory, it is possible to compute the probability (
P
) of a particle’s moving a certain distance (
x
) in any given direction (the total distance it moves will be greater than
x
) during a certain time interval (
t
) in a medium whose coefficient of diffusion (
D
) is known,
D
being equal to one-half the average of the square of the
displacement
in the
x
-direction. This formula for probability “density” allows
P
to be plotted against
x
. The graph is the familiar
bell-shaped Gaussian “normal” curve
that typically arises when the
random variable
is the sum of many independent, statistically identical random variables, in this case the many little pushes that add up to the total motion. The equation for this relationship is
Also called:
Brownian movement
Trusted knowledge for those who want to know more.
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The introduction of the
ultramicroscope
in 1903 aided quantitative studies by making visible small colloidal particles whose greater activity could be measured more easily. Several important measurements of this kind were made from 1905 to 1911. During this period the French physicist
Jean-Baptiste Perrin
was successful in verifying Einstein’s analysis, and for this work he was awarded the
Nobel Prize
for Physics in 1926. His work established the physical theory of Brownian motion and ended the
skepticism
about the existence of atoms and molecules as actual physical entities.
This article was most recently revised and updated by
Erik Gregersen
. |
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- [Introduction](https://www.britannica.com/science/Brownian-motion)
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[Brownian particle](https://cdn.britannica.com/20/6920-050-C12AFEF7/particle-motion-discrepancy-pressures-Brownian-surfaces.jpg) (Left) Random motion of a Brownian particle and (right) random discrepancy between the molecular pressures on different surfaces of the particle that cause motion.
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# Brownian motion
physics
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Also known as: Brownian movement
Written and fact-checked by
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Top Questions
- What is Brownian motion?
- Who discovered Brownian motion and how?
- What causes Brownian motion to happen?
- How can we observe Brownian motion in everyday life?
- Why was the explanation of Brownian motion important for science?
- How does Brownian motion support the idea that atoms and molecules exist?
Show more
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**Brownian motion**, any of various physical phenomena in which some quantity is constantly undergoing small, random fluctuations. It was named for the Scottish botanist [Robert Brown](https://www.britannica.com/biography/Robert-Brown-Scottish-botanist), the first to study such fluctuations (1827).
If a number of particles subject to Brownian motion are present in a given medium and there is no preferred direction for the random oscillations, then over a period of time the particles will tend to be spread evenly throughout the medium. Thus, if *A* and *B* are two [adjacent](https://www.merriam-webster.com/dictionary/adjacent) regions and, at time *t*, *A* contains twice as many particles as *B*, at that instant the probability of a particle’s leaving *A* to enter *B* is twice as great as the probability that a particle will leave *B* to enter *A*. The physical process in which a substance tends to spread steadily from regions of high concentration to regions of lower concentration is called [diffusion](https://www.britannica.com/science/diffusion). [Diffusion](https://www.merriam-webster.com/dictionary/Diffusion) can therefore be considered a macroscopic [manifestation](https://www.merriam-webster.com/dictionary/manifestation) of Brownian [motion](https://www.britannica.com/science/motion-mechanics) on the microscopic level. Thus, it is possible to study diffusion by simulating the motion of a Brownian particle and computing its average behaviour. A few examples of the countless diffusion processes that are studied in terms of Brownian motion include the diffusion of pollutants through the [atmosphere](https://www.britannica.com/science/atmosphere), the diffusion of “holes” (minute regions in which the [electrical charge](https://www.britannica.com/science/electric-charge) potential is positive) through a [semiconductor](https://www.britannica.com/science/semiconductor), and the diffusion of calcium through bone tissue in living organisms.
## Early investigations
The term “classical Brownian motion” describes the random movement of microscopic particles suspended in a [liquid](https://www.britannica.com/science/liquid-state-of-matter) or [gas](https://www.britannica.com/science/gas-state-of-matter). Brown was investigating the fertilization process in *Clarkia pulchella*, then a newly discovered species of [flowering plant](https://www.britannica.com/plant/angiosperm), when he noticed a “rapid oscillatory motion” of the microscopic particles within the [pollen](https://www.britannica.com/science/pollen) grains suspended in water under the [microscope](https://www.britannica.com/technology/microscope). Other researchers had noticed this phenomenon earlier, but Brown was the first to study it. Initially he believed that such motion was a [vital](https://www.britannica.com/dictionary/vital) activity peculiar to the male sex cells of plants, but he then checked to see if the pollen of plants dead for over a century showed the same movement. Brown called this a “very unexpected fact of seeming vitality being retained by these ‘molecules’ so long after the death of the plant.” Further study revealed that the same motion could be observed not only with particles of other organic substances but even with chips of glass or granite and particles of smoke. Finally, in inarguable support of the nonliving nature of the phenomenon, he demonstrated it in fluid-filled vesicles in rock from the [Great Sphinx](https://www.britannica.com/topic/sphinx).
[ Britannica Quiz Physics and Natural Law](https://www.britannica.com/quiz/physics-and-natural-law)
Early explanations [attributed](https://www.britannica.com/dictionary/attributed) the motion to thermal [convection](https://www.britannica.com/science/convection) currents in the [fluid](https://www.britannica.com/science/fluid-physics). When observation showed that nearby particles exhibited totally uncorrelated activity, however, this simple explanation was abandoned. By the 1860s theoretical physicists had become interested in Brownian motion and were searching for a consistent explanation of its various characteristics: a given particle appeared equally likely to move in any direction; further motion seemed totally unrelated to past motion; and the motion never stopped. An experiment (1865) in which a suspension was sealed in glass for a year showed that the Brownian motion persisted. More [systematic](https://www.britannica.com/dictionary/systematic) investigation in 1889 determined that small particle size and low viscosity of the surrounding fluid resulted in faster motion.
## [Einstein](https://www.britannica.com/biography/Albert-Einstein)’s theory of Brownian motion
Since higher temperatures also led to more-rapid Brownian motion, in 1877 it was suggested that its cause lay in the “thermal molecular motion in the liquid environment.” The idea that molecules of a liquid or gas are constantly in motion, colliding with each other and bouncing back and forth, is a prominent part of the [kinetic theory of gases](https://www.britannica.com/science/kinetic-theory-of-gases) developed in the third quarter of the 19th century by the physicists [James Clerk Maxwell](https://www.britannica.com/biography/James-Clerk-Maxwell), [Ludwig Boltzmann](https://www.britannica.com/biography/Ludwig-Boltzmann), and [Rudolf Clausius](https://www.britannica.com/biography/Rudolf-Clausius) in explanation of heat phenomena. According to the theory, the [temperature](https://www.britannica.com/science/temperature) of a substance is proportional to the average [kinetic energy](https://www.britannica.com/science/kinetic-energy) with which the molecules of the substance are moving or vibrating. It was natural to guess that somehow this motion might be imparted to larger particles that could be observed under the microscope; if true, this would be the first directly observable effect that would [corroborate](https://www.merriam-webster.com/dictionary/corroborate) the kinetic theory. This line of reasoning led the German physicist [Albert Einstein](https://www.britannica.com/biography/Albert-Einstein) in 1905 to produce his quantitative theory of Brownian motion. Similar studies were carried out on Brownian motion, independently and almost at the same time, by the Polish physicist Marian Smoluchowski, who used methods somewhat different from Einstein’s.
[](https://www.britannica.com/video/Albert-Einstein-Description-motion-theory-size-Brownian/-203883)
Learn about Albert Einstein's theory of Brownian motion and how he derived the size of atoms based on how much the Brownian particles moveDescription of Albert Einstein's theory of Brownian motion and how he derived the size of atoms.
(more)
[See all videos for this article](https://www.britannica.com/science/Brownian-motion/images-videos)
Einstein wrote later that his major aim was to find facts that would guarantee as much as possible the existence of [atoms](https://www.britannica.com/science/atom) of definite size. In the midst of this work, he discovered that according to [atomic theory](https://www.britannica.com/science/atomic-theory) there would have to be an observable movement of suspended microscopic particles. Einstein did not realize that observations concerning the Brownian motion were already long familiar. Reasoning on the basis of [statistical mechanics](https://www.britannica.com/science/statistical-mechanics), he showed that for such a microscopic particle the random difference between the pressure of molecular bombardment on two opposite sides would cause it to constantly [wobble](https://www.britannica.com/dictionary/wobble) back and forth. A smaller particle, a less viscous fluid, and a higher temperature would each increase the amount of motion one could expect to observe. Over a period of time, the particle would tend to drift from its starting point, and, on the basis of kinetic theory, it is possible to compute the probability (*P*) of a particle’s moving a certain distance (*x*) in any given direction (the total distance it moves will be greater than *x*) during a certain time interval (*t*) in a medium whose coefficient of diffusion (*D*) is known, *D* being equal to one-half the average of the square of the [displacement](https://www.britannica.com/dictionary/displacement) in the *x*\-direction. This formula for probability “density” allows *P* to be plotted against *x*. The graph is the familiar [bell-shaped Gaussian “normal” curve](https://www.britannica.com/science/bell-curve) that typically arises when the [random variable](https://www.britannica.com/topic/random-variable) is the sum of many independent, statistically identical random variables, in this case the many little pushes that add up to the total motion. The equation for this relationship is
Also called:
Brownian movement
*(Show more)*
Key People:
[Albert Einstein](https://www.britannica.com/biography/Albert-Einstein)
[Robert Brown](https://www.britannica.com/biography/Robert-Brown-Scottish-botanist)
[Wendelin Werner](https://www.britannica.com/biography/Wendelin-Werner)
[Jean Perrin](https://www.britannica.com/biography/Jean-Perrin)
*(Show more)*
Related Topics:
[motion](https://www.britannica.com/science/motion-mechanics)
[kinetic theory](https://www.britannica.com/science/kinetic-theory)
*(Show more)*
[See all related content](https://www.britannica.com/facts/Brownian-motion)
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The introduction of the [ultramicroscope](https://www.britannica.com/technology/ultramicroscope) in 1903 aided quantitative studies by making visible small colloidal particles whose greater activity could be measured more easily. Several important measurements of this kind were made from 1905 to 1911. During this period the French physicist [Jean-Baptiste Perrin](https://www.britannica.com/biography/Jean-Perrin) was successful in verifying Einstein’s analysis, and for this work he was awarded the [Nobel Prize](https://www.britannica.com/topic/Nobel-Prize) for Physics in 1926. His work established the physical theory of Brownian motion and ended the [skepticism](https://www.merriam-webster.com/dictionary/skepticism) about the existence of atoms and molecules as actual physical entities.
This article was most recently revised and updated by [Erik Gregersen](https://www.britannica.com/editor/Erik-Gregersen/6723).
Britannica AI
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Brownian motion
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[diffusion](https://www.britannica.com/science/diffusion)
[Introduction](https://www.britannica.com/science/diffusion) [References & Edit History](https://www.britannica.com/science/diffusion/additional-info) [Related Topics](https://www.britannica.com/facts/diffusion)
[Images & Videos](https://www.britannica.com/science/diffusion/images-videos)
[](https://cdn.britannica.com/58/54958-050-3FD49C7E/membrane-concentration-Diffusion-ions-KCl-side-voltage.jpg) [](https://cdn.britannica.com/03/3503-004-B40B83E3/spread-cloud-particles-point-value-curve-n.jpg) [](https://cdn.britannica.com/56/54956-050-D3A9A6D0/Water-Diffusion-side-water-membrane-concentration-gradient.jpg)
[](https://www.britannica.com/video/Video-roots-substances-soil-osmosis-transport-diffusion/-16696)
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[Ion movement across a semipermeable membrane](https://cdn.britannica.com/58/54958-050-3FD49C7E/membrane-concentration-Diffusion-ions-KCl-side-voltage.jpg) Diffusion of ions across a semipermeable membrane. (A) A high concentration of KCl is placed on side 1, opposite a semipermeable membrane from a low concentration. The membrane allows only K\+ to diffuse, thereby establishing an electrical potential difference across the membrane. (B) The separation of charge creates an electrostatic voltage force, which draws some K\+ back to side 1. (C) At equilibrium, there is no net flux of K\+ in either direction. Side 1, with the higher concentration of KCl, has a negative charge compared with side 2.
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# diffusion
physics
Homework Help
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Mar. 10, 2026
•[History](https://www.britannica.com/science/diffusion/additional-info#history)
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**diffusion**, process resulting from random [motion](https://www.britannica.com/science/motion-mechanics) of [molecules](https://www.britannica.com/science/molecule) by which there is a net flow of [matter](https://www.britannica.com/science/matter) from a region of high [concentration](https://www.britannica.com/science/concentration-chemistry) to a region of low concentration. A familiar example is the perfume of a [flower](https://www.britannica.com/science/flower) that quickly permeates the still air of a room.
[Heat](https://www.britannica.com/science/heat) [conduction](https://www.britannica.com/science/thermal-conduction) in fluids involves [thermal energy](https://www.britannica.com/science/thermal-energy) transported, or diffused, from higher to lower [temperature](https://www.britannica.com/science/temperature). Operation of a [nuclear reactor](https://www.britannica.com/technology/nuclear-reactor) involves the [diffusion](https://www.merriam-webster.com/dictionary/diffusion) of [neutrons](https://www.britannica.com/science/neutron) through a medium that causes frequent [scattering](https://www.britannica.com/science/scattering) but only rare [absorption](https://www.britannica.com/science/absorption-physics) of neutrons.
Related Topics:
[osmosis](https://www.britannica.com/science/osmosis)
[diffusion equation](https://www.britannica.com/science/diffusion-equation)
[diffusion coefficient](https://www.britannica.com/science/diffusion-coefficient)
[thermal diffusion](https://www.britannica.com/science/thermal-diffusion)
[Loschmidt diffusion tube](https://www.britannica.com/science/Loschmidt-diffusion-tube)
*(Show more)*
On the Web:
[Chemistry LibreTexts - Diffusion](https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Introduction_to_Solid_State_Chemistry/01%3A_Lectures/1.09%3A_Diffusion) (Mar. 10, 2026)
*(Show more)*
[See all related content](https://www.britannica.com/facts/diffusion)
The rate of flow of the diffusing substance is found to be proportional to the concentration [gradient](https://www.britannica.com/science/gradient-mathematics). If *j* is the amount of substance passing through a reference surface of unit area per unit time, if the coordinate *x* is perpendicular to this reference area, if *c* is the concentration of the substance, and if the constant of proportionality is *D,* then *j* = −*D*(*dc*/*dx*); *dc*/*dx* is the rate of change of concentration in the direction *x,* and the minus sign indicates the flow is from higher to lower concentration. *D* is called the [diffusivity](https://www.britannica.com/science/diffusivity) and governs the rate of diffusion.
[ More From Britannica principles of physical science: Diffusion](https://www.britannica.com/science/principles-of-physical-science/Examples-of-differential-equations-for-fields#ref366360)
[The Editors of Encyclopaedia Britannica](https://www.britannica.com/editor/The-Editors-of-Encyclopaedia-Britannica/4419)This article was most recently revised and updated by [Erik Gregersen](https://www.britannica.com/editor/Erik-Gregersen/6723).
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| Readable Markdown | Top Questions
- What is Brownian motion?
- Who discovered Brownian motion and how?
- What causes Brownian motion to happen?
- How can we observe Brownian motion in everyday life?
- Why was the explanation of Brownian motion important for science?
- How does Brownian motion support the idea that atoms and molecules exist?
**Brownian motion**, any of various physical phenomena in which some quantity is constantly undergoing small, random fluctuations. It was named for the Scottish botanist [Robert Brown](https://www.britannica.com/biography/Robert-Brown-Scottish-botanist), the first to study such fluctuations (1827).
If a number of particles subject to Brownian motion are present in a given medium and there is no preferred direction for the random oscillations, then over a period of time the particles will tend to be spread evenly throughout the medium. Thus, if *A* and *B* are two [adjacent](https://www.merriam-webster.com/dictionary/adjacent) regions and, at time *t*, *A* contains twice as many particles as *B*, at that instant the probability of a particle’s leaving *A* to enter *B* is twice as great as the probability that a particle will leave *B* to enter *A*. The physical process in which a substance tends to spread steadily from regions of high concentration to regions of lower concentration is called [diffusion](https://www.britannica.com/science/diffusion). [Diffusion](https://www.merriam-webster.com/dictionary/Diffusion) can therefore be considered a macroscopic [manifestation](https://www.merriam-webster.com/dictionary/manifestation) of Brownian [motion](https://www.britannica.com/science/motion-mechanics) on the microscopic level. Thus, it is possible to study diffusion by simulating the motion of a Brownian particle and computing its average behaviour. A few examples of the countless diffusion processes that are studied in terms of Brownian motion include the diffusion of pollutants through the [atmosphere](https://www.britannica.com/science/atmosphere), the diffusion of “holes” (minute regions in which the [electrical charge](https://www.britannica.com/science/electric-charge) potential is positive) through a [semiconductor](https://www.britannica.com/science/semiconductor), and the diffusion of calcium through bone tissue in living organisms.
## Early investigations
The term “classical Brownian motion” describes the random movement of microscopic particles suspended in a [liquid](https://www.britannica.com/science/liquid-state-of-matter) or [gas](https://www.britannica.com/science/gas-state-of-matter). Brown was investigating the fertilization process in *Clarkia pulchella*, then a newly discovered species of [flowering plant](https://www.britannica.com/plant/angiosperm), when he noticed a “rapid oscillatory motion” of the microscopic particles within the [pollen](https://www.britannica.com/science/pollen) grains suspended in water under the [microscope](https://www.britannica.com/technology/microscope). Other researchers had noticed this phenomenon earlier, but Brown was the first to study it. Initially he believed that such motion was a [vital](https://www.britannica.com/dictionary/vital) activity peculiar to the male sex cells of plants, but he then checked to see if the pollen of plants dead for over a century showed the same movement. Brown called this a “very unexpected fact of seeming vitality being retained by these ‘molecules’ so long after the death of the plant.” Further study revealed that the same motion could be observed not only with particles of other organic substances but even with chips of glass or granite and particles of smoke. Finally, in inarguable support of the nonliving nature of the phenomenon, he demonstrated it in fluid-filled vesicles in rock from the [Great Sphinx](https://www.britannica.com/topic/sphinx).
[ Britannica Quiz Physics and Natural Law](https://www.britannica.com/quiz/physics-and-natural-law)
Early explanations [attributed](https://www.britannica.com/dictionary/attributed) the motion to thermal [convection](https://www.britannica.com/science/convection) currents in the [fluid](https://www.britannica.com/science/fluid-physics). When observation showed that nearby particles exhibited totally uncorrelated activity, however, this simple explanation was abandoned. By the 1860s theoretical physicists had become interested in Brownian motion and were searching for a consistent explanation of its various characteristics: a given particle appeared equally likely to move in any direction; further motion seemed totally unrelated to past motion; and the motion never stopped. An experiment (1865) in which a suspension was sealed in glass for a year showed that the Brownian motion persisted. More [systematic](https://www.britannica.com/dictionary/systematic) investigation in 1889 determined that small particle size and low viscosity of the surrounding fluid resulted in faster motion.
## [Einstein](https://www.britannica.com/biography/Albert-Einstein)’s theory of Brownian motion
Since higher temperatures also led to more-rapid Brownian motion, in 1877 it was suggested that its cause lay in the “thermal molecular motion in the liquid environment.” The idea that molecules of a liquid or gas are constantly in motion, colliding with each other and bouncing back and forth, is a prominent part of the [kinetic theory of gases](https://www.britannica.com/science/kinetic-theory-of-gases) developed in the third quarter of the 19th century by the physicists [James Clerk Maxwell](https://www.britannica.com/biography/James-Clerk-Maxwell), [Ludwig Boltzmann](https://www.britannica.com/biography/Ludwig-Boltzmann), and [Rudolf Clausius](https://www.britannica.com/biography/Rudolf-Clausius) in explanation of heat phenomena. According to the theory, the [temperature](https://www.britannica.com/science/temperature) of a substance is proportional to the average [kinetic energy](https://www.britannica.com/science/kinetic-energy) with which the molecules of the substance are moving or vibrating. It was natural to guess that somehow this motion might be imparted to larger particles that could be observed under the microscope; if true, this would be the first directly observable effect that would [corroborate](https://www.merriam-webster.com/dictionary/corroborate) the kinetic theory. This line of reasoning led the German physicist [Albert Einstein](https://www.britannica.com/biography/Albert-Einstein) in 1905 to produce his quantitative theory of Brownian motion. Similar studies were carried out on Brownian motion, independently and almost at the same time, by the Polish physicist Marian Smoluchowski, who used methods somewhat different from Einstein’s.
Learn about Albert Einstein's theory of Brownian motion and how he derived the size of atoms based on how much the Brownian particles moveDescription of Albert Einstein's theory of Brownian motion and how he derived the size of atoms.
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Einstein wrote later that his major aim was to find facts that would guarantee as much as possible the existence of [atoms](https://www.britannica.com/science/atom) of definite size. In the midst of this work, he discovered that according to [atomic theory](https://www.britannica.com/science/atomic-theory) there would have to be an observable movement of suspended microscopic particles. Einstein did not realize that observations concerning the Brownian motion were already long familiar. Reasoning on the basis of [statistical mechanics](https://www.britannica.com/science/statistical-mechanics), he showed that for such a microscopic particle the random difference between the pressure of molecular bombardment on two opposite sides would cause it to constantly [wobble](https://www.britannica.com/dictionary/wobble) back and forth. A smaller particle, a less viscous fluid, and a higher temperature would each increase the amount of motion one could expect to observe. Over a period of time, the particle would tend to drift from its starting point, and, on the basis of kinetic theory, it is possible to compute the probability (*P*) of a particle’s moving a certain distance (*x*) in any given direction (the total distance it moves will be greater than *x*) during a certain time interval (*t*) in a medium whose coefficient of diffusion (*D*) is known, *D* being equal to one-half the average of the square of the [displacement](https://www.britannica.com/dictionary/displacement) in the *x*\-direction. This formula for probability “density” allows *P* to be plotted against *x*. The graph is the familiar [bell-shaped Gaussian “normal” curve](https://www.britannica.com/science/bell-curve) that typically arises when the [random variable](https://www.britannica.com/topic/random-variable) is the sum of many independent, statistically identical random variables, in this case the many little pushes that add up to the total motion. The equation for this relationship is
Also called:
Brownian movement
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The introduction of the [ultramicroscope](https://www.britannica.com/technology/ultramicroscope) in 1903 aided quantitative studies by making visible small colloidal particles whose greater activity could be measured more easily. Several important measurements of this kind were made from 1905 to 1911. During this period the French physicist [Jean-Baptiste Perrin](https://www.britannica.com/biography/Jean-Perrin) was successful in verifying Einstein’s analysis, and for this work he was awarded the [Nobel Prize](https://www.britannica.com/topic/Nobel-Prize) for Physics in 1926. His work established the physical theory of Brownian motion and ended the [skepticism](https://www.merriam-webster.com/dictionary/skepticism) about the existence of atoms and molecules as actual physical entities.
This article was most recently revised and updated by [Erik Gregersen](https://www.britannica.com/editor/Erik-Gregersen/6723). |
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