De Broglie Wavelength Of A Gas Molecule — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
De Broglie Wavelength of a Gas Molecule The formula is valid for ideal gas molecules at absolute temperature T, assuming non-relativistic speeds and non-interacting particles. From de Broglie's hypothesis: = h / p. For an ideal gas molecule, the average translational kinetic energy is E = (3/2)kT. Relate momentum to kinetic energy: p = 2mE . Substitute E into the momentum equation: p = 2m(3/2kT) = 3mkT . Substitute p back into the de Broglie equation: = h / 3mkT . Temperature T must be greater than 0 K. The particle must behave as an ideal gas molecule. The speed of the molecule is non-relativistic (v << c). Confusing the kinetic energy of a gas molecule ((3/2)kT) with energy per degree of freedom ((1/2)kT). Using the mass of a mole instead of the mass of a single molecule (m). Applying the formula to relativistic particles.