Assume that a room at sea level is filled with a gas of nitrogen molecules N2 in thermal equilibrium at -10.0 °C (negative ten degrees Celsius). There are 7 protons and 7 neutrons in the nucleus of a nitrogen atom N. You may take the masses of the proton and the neutron to be the same, and ignore the mass of the electrons. 1 atm=1.01x105 N/m² , h=1.05x10 34 J-s , m,=1.67x10-27 kg, ke = 1.38x1023 J/K . a) What is the (particle) number density n according to the ideal gas law? b) Compare the number density n with the quantum concentration ng at the same temperature. c) Is the gas in the classical or quantum regime?

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Assume that a room at sea level is filled with a gas of nitrogen molecules N2
in thermal equilibrium at -10.0 °C (negative ten degrees Celsius). There are 7 protons and 7
neutrons in the nucleus of a nitrogen atom N. You may take the masses of the proton and the
neutron to be the same, and ignore the mass of the electrons. 1 atm=1.01x105 N/m² ,
h=1.05x10-34 J-s , mp=1.67x10-27 kg, kB = 1.38x10-23 J/K .
a) What is the (particle) number density n according to the ideal gas law?
b) Compare the number density n with the quantum concentration ng at the same
temperature.
c) Is the gas in the classical or quantum regime?
Transcribed Image Text:Assume that a room at sea level is filled with a gas of nitrogen molecules N2 in thermal equilibrium at -10.0 °C (negative ten degrees Celsius). There are 7 protons and 7 neutrons in the nucleus of a nitrogen atom N. You may take the masses of the proton and the neutron to be the same, and ignore the mass of the electrons. 1 atm=1.01x105 N/m² , h=1.05x10-34 J-s , mp=1.67x10-27 kg, kB = 1.38x10-23 J/K . a) What is the (particle) number density n according to the ideal gas law? b) Compare the number density n with the quantum concentration ng at the same temperature. c) Is the gas in the classical or quantum regime?
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