Discussion  Fr 04.11.2005 at 12:15,  HR 30.1  

Home work 1
 
 

Exercise 1:  De Broglie wavelength

Consider a He gas at room temperature. As you know, helium is a single-atomic gas. The mean kinetic energy of each atom at the temperature T is E = ³/₂ kT, where k is the Boltzmann constant. 

a. Calculate the mean velocity of a helium atom, v in cm/s. Calculate the de Broglie wavelength λ in cm which corresponds to this velocity. Assuming the normal atmospheric pressure, calculate the mean distance between helium atoms d and compare this distance with the de Broglie wavelength. One may expect that the quantum effects can be important if l ³ d, otherwise, the classical description should be used. Which case is realized for the helium gas?  What one should expect decreasing/increasing the temperature and the gas pressure?

b. The density of liquid helium is 0.15 g/cm³. Following the previous problem compare the mean distance between the atoms d with the de Broglie wavelength λ at the temperature T = 0.01K. 
 

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