Helium gas is kept at and atmospheric pressure

PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

Helium gas is kept at 300 K300\,\text{K} and atmospheric pressure 1.01×105 Pa1.01\times10^{5}\,\text{Pa}. The molar mass of helium is 4.0 g mol−14.0\,\text{g\,mol}^{-1} and the gas constant is R=8.31 J mol−1 K−1R=8.31\,\text{J\,mol}^{-1}\,\text{K}^{-1}. Take Boltzmann constant kB=1.38×10−23 J K−1k_{\text B}=1.38\times10^{-23}\,\text{J\,K}^{-1}. (a) Treating helium as an ideal gas, estimate the average volume available to each helium atom at the given conditions. (b) From the result of part (a), obtain the order of magnitude of the mean separation between neighbouring atoms. (c) Using the root-mean-square speed corresponding to temperature TT, calculate the de Broglie wavelength of a helium atom at 300 K300\,\text{K}. (d) Compare the wavelength from part (c) with the mean separation from part (b) and discuss whether quantum-mechanical wave effects are likely to influence the macroscopic behaviour of the gas at room temperature.

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