Random Molecular Motion
Particles bounce inside a box, faster as T rises.
Key Notes
Kinetic theory: gas molecules are in constant random motion, colliding elastically with each other and walls.
Random direction at any instant; speeds follow a Maxwell-Boltzmann distribution.
Brownian motion (1827): tiny particles suspended in fluid show random jiggle — direct evidence of molecular collisions.
No preferred direction in a gas at equilibrium — isotropic.
Average velocity of a gas at rest = 0 (vectors cancel). Average SPEED ≠ 0.
Diffusion: net transport of molecules from high to low concentration due to random motion.
Effusion (Graham's law): rate of effusion ∝ 1/√M — lighter gases escape faster.
Random walks: in time t, average displacement scales as √t (not t).
Formulas
Average velocity (vector)
Equal probability in all directions ⇒ vector sum zero.
Average speed (scalar)
Non-zero, depends on T and mass.
Random walk distance
Diffusion grows linearly in time.
Graham's law
Effusion rate inversely proportional to √M.
Important Points
At equilibrium: vector velocity sums to zero — gas at rest macroscopically.
Brownian motion is direct visual evidence of random molecular collisions.
Random motion is fundamental to gas behavior — explains pressure, temperature, diffusion.
Diffusion is SLOW: small molecules in air diffuse ~cm in seconds; perfumes in still air over ~minutes.
In a sealed container: molecules continuously bounce — pressure is uniform on average.
Lighter gases (H₂, He) move faster at same T ⇒ diffuse and effuse faster.
Random Molecular Motion notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.