In a gas at (absolute) temperature t, the molecules have a typical kinetic energy of 3kbt/2, where kb is boltzmann’s constant.
derive an expression for the thermal debroglie wavelength, a typical value for the debroglie wavelength λ of a molecule in the gas.
for helium atoms, calculate the debroglie wavelength at room temperature and at the boiling point of helium, and compare each number with the typical distance between the particles in each state.
comment on when we will need to use quantum mechanics in understanding the behavior of helium.