6.
A helium atom is heavier than a hydrogen molecule. At 298 K, the average kinetic energy
of a helium atom is
a. twice that of a hydrogen molecule
b. equal to that of a hydrogen molecule
c. four times that of a hydrogen molecule
d. half that of a hydrogen molecule
Helium Atom vs Hydrogen Molecule Kinetic Energy at 298 K
CSIR NET Solved Concept
The average kinetic energy of a helium atom equals that of a hydrogen molecule at 298 K,
despite helium being heavier. This follows from the kinetic theory of gases,
where average kinetic energy depends solely on temperature.
Core Concept
The average translational kinetic energy per molecule in an ideal gas is given by:
KE = (3/2) kT
where k is Boltzmann’s constant and T is the absolute temperature in Kelvin.
Both helium (He, monatomic) and hydrogen (H₂, diatomic) follow this for translational motion
at the same temperature T = 298 K.
Mass differences affect speed (vrms = √(3kT/m)),
but not the average kinetic energy, since:
KE = (1/2)mvrms2 = (3/2)kT
Option Analysis
“Twice” would imply double the temperature or different degrees of freedom, which does not apply here.
KEHe = (3/2)k(298) = KEH₂.
Helium has a mass of 4 u, while H₂ has 2 u, but kinetic energy depends only on temperature, not mass.
the factor of four arises from mass ratio effects on molecular speeds, not on kinetic energy.
half would occur if temperature were halved, but here the temperature is the same.
