Q.Write a short note on Brownian movement.
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Brownian Motion: From Intuition to Precision
Imagine you are in a completely dark room, completely still, and someone throws a hundred ping-pong balls at you from random directions every second. You wouldn't stand still — you'd jerk, stumble, and lurch in a chaotic, unpredictable path. That is the essence of Brownian motion.
In 1827, the botanist Robert Brown looked through his microscope at pollen grains suspended in water. He expected to see them sit still. Instead, they danced — a continuous, jittery, random zig-zag. Brown had no explanation. The real insight came decades later: the water molecules themselves are in constant, violent thermal motion. A pollen grain, though huge compared to a single water molecule, is tiny enough to feel the imbalance of these molecular impacts. At any instant, a few more molecules might hit it from the left than from the right, shoving it sideways. A moment later, the imbalance shifts, and it lurches another way. The result is the random walk we call Brownian motion.
Brownian motion is not caused by the pollen grain being alive. It is a purely physical phenomenon — a direct, visible consequence of the kinetic theory of matter. Any sufficiently small particle (about 1μm to 10μm in size) suspended in a fluid will exhibit it.
The Intuition: Why "Unbalanced Bombardment"?
A colloidal particle is constantly struck by molecules of the surrounding medium (water, air, etc.). These molecules move at hundreds of metres per second. If the particle were enormous, the billions of trillions of impacts per second would average out perfectly — net force zero, particle stationary. But for a tiny particle, the number of impacts is smaller, and the statistical fluctuations become significant.
Think of a coin toss. Toss a coin 10 times — you might easily get 7 heads and 3 tails (a 4-toss imbalance). Toss it 10,000 times — the imbalance is tiny in percentage terms. The colloidal particle experiences the "7 heads, 3 tails" version of molecular bombardment. That momentary net force shoves it. The next moment, the imbalance is in a different direction. Hence the zig-zag.
A useful mental model: Brownian motion is the random walk of a particle. In each tiny time interval, the particle takes a step of random direction and (roughly) constant length. The path it traces is continuous but nowhere differentiable — it has no well-defined tangent at any point. It is infinitely kinky.
The Precise Statement
Mathematically, Brownian motion is formalised as the Wiener process W(t) (or B(t)). It is a continuous-time stochastic process satisfying:
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W(0)=0 almost surely. The motion starts at the origin.
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Independent increments. For any non-overlapping time intervals [t1,t2] and [t3,t4], the displacements W(t2)−W(t1) and W(t4)−W(t3) are independent random variables. What the particle does in one interval has no memory of what it did in another.
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Gaussian increments. For any 0≤s<t, the displacement W(t)−W(s) is normally distributed with mean 0 and variance t−s:
W(t)−W(s)∼N(0,t−s).
The spread of possible positions grows as the square root of the elapsed time.
- Continuous paths. The function t↦W(t) is continuous with probability 1. The particle never teleports — its path is an unbroken line, however wild.
The probability density of finding a Brownian particle at position x at time t, given it started at x=0 at t=0, is:
P(x,t)=2πt1e−x2/(2t)
This is the diffusion equation solution — Brownian motion is the microscopic mechanism behind macroscopic diffusion.
Key Properties (Exam-Ready)
- Mean displacement is zero: ⟨W(t)⟩=0. On average, the particle goes nowhere. …
When a colloidal sol is viewed under an ultramicroscope, its dispersed particles are seen in constant erratic motion -- a phenomenon with both a specific cause and a stabilising effect. …
Brownian movement is the random zig-zag motion of colloidal particles caused by unequal molecular bombardment by the dispersion medium; it stabilises the sol against settling.
Brownian movement (named after Robert Brown):
When a colloidal solution (sol) is viewed under an ultramicroscope, the colloidal particles are seen to be in continuous, rapid, random, zig-zag motion in all directions.
Cause: The colloidal particles are constantly and unequally bombarded by the fast-moving molecules of the dispersion medium. At any instant the impacts from different sides are unbalanced, giving the particle a net push that keeps changing direction — producing the zig-zag motion. Smaller particles and less viscous media show faster Brownian motion.
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- CBSE 2026Set A2 marksQ.Write a short note on Brownian movement.
›Reveal solutionSolution
Brownian movement is the random zig-zag motion of colloidal particles caused by unequal molecular bombardment by the dispersion medium; it stabilises the sol against settling.
Brownian movement (named after Robert Brown):
When a colloidal solution (sol) is viewed under an ultramicroscope, the colloidal particles are seen to be in continuous, rapid, random, zig-zag motion in all directions.
Cause: The colloidal particles are constantly and unequally bombarded by the fast-moving molecules of the dispersion medium. At any instant the impacts from different sides are unbalanced, giving the particle a net push that keeps changing direction — producing the zig-zag motion. Smaller particles and less viscous media show faster Brownian motion.
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- CBSE 2026Set ANNUAL2 marksQ.Write the factors affecting Brownian Motion.
›Reveal solutionSolution
Brownian motion depends chiefly on the temperature of the fluid, the size (mass) of the suspended particles, and the viscosity of the medium.
Brownian motion is the continuous, random, zig-zag movement of tiny particles suspended in a fluid (liquid or gas), caused by their being repeatedly and unevenly bombarded by the fast-moving molecules of the surrounding fluid. The main factors affecting how vigorous this motion is are:
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Temperature of the medium: At higher temperature, the fluid molecules move faster (higher average kinetic energy), so they strike the suspended particles more forcefully and more frequently, making the Brownian motion more vigorous. Lower temperature reduces it.
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Size (and mass) of the suspended particles: Smaller and lighter particles are more easily jostled about by molecular collisions (since a given impulse produces a larger change in velocity for a smaller mass), so they show more pronounced Brownian motion. Larger, heavier particles show comparatively less erratic motion because the many random collisions tend to average out over a larger surface/mass.
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- CBSE 2024Set D2 marksQ.What is Brownian movement?
›Reveal solutionSolution
Brownian movement is the ceaseless random zig-zag motion of colloidal particles, caused by uneven bombardment by dispersion-medium molecules; it keeps colloids stable.
When a colloidal solution (sol) is viewed under an ultramicroscope, the colloidal particles are seen to be in continuous, rapid, random zig-zag motion. This motion is called Brownian movement (first observed by Robert Brown).
Cause: The colloidal particles are constantly struck from all sides by the molecules of the dispersion medium. Because these collisions are unequal (unbalanced) at any instant, the particle is pushed in a random direction, giving the characteristic zig-zag path.
Significance: …
- CBSE 2024Set ANNUAL2 marksQ.Write the factors affecting Brownian Motion.
›Reveal solutionSolution
Brownian motion depends mainly on particle size, fluid temperature, and fluid viscosity — smaller particles, higher temperature, and lower viscosity all make the motion more vigorous.
Brownian motion is the continuous, random, zig-zag motion of microscopic particles suspended in a fluid, caused by unequal bombardment from the surrounding fluid molecules.
The factors affecting it are:
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Size (and mass) of the suspended particles: smaller and lighter particles show more vigorous Brownian motion, because the random molecular impacts are less likely to average out to zero for a light particle.
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Temperature of the fluid: higher temperature means faster-moving fluid molecules, giving more energetic, more frequent impacs, so Brownian motion increases with temperature.
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- CBSE 2019Set ANNUAL2 marksQ.List the factors affecting Brownian motion.
›Reveal solutionSolution
Brownian motion is influenced chiefly by temperature, particle size, and the viscosity of the surrounding medium.
Brownian motion is the continuous, random, zig-zag motion of tiny particles suspended in a fluid (liquid or gas), caused by the particles being unevenly bombarded on all sides by the constantly, randomly moving molecules of the fluid. The factors that affect how vigorous this motion is include:
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Temperature of the medium: Higher temperature means the fluid molecules move faster (greater average kinetic energy), so they strike the suspended particles harder and more frequently, making the Brownian motion more vigorous.
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Size of the suspended particles: Smaller/lighter particles are more easily jostled and show more pronounced, rapid Brownian motion, because the same molecular impacts produce a larger acceleration on a smaller mass; larger/heavier particles show much less noticeable Brownian motion.
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