Determining the Temperature of a Hydrogen Gas

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SUMMARY

The discussion centers on calculating the temperature of a hydrogen gas with 5% of its atoms in the n=2 quantum state. The relevant energy equation for this scenario is E = (5/2)kT, acknowledging that hydrogen is treated as a monatomic gas rather than diatomic. The Boltzmann factor, exp(-E/kT) = 0.05, is crucial for determining the temperature. Participants emphasize the need to correctly identify the energy levels and the implications of quantum states on temperature calculations.

PREREQUISITES
  • Understanding of quantum states and energy levels in hydrogen atoms
  • Familiarity with the Boltzmann distribution and its application
  • Knowledge of thermodynamic principles, specifically relating to monatomic gases
  • Basic grasp of statistical mechanics and kinetic theory
NEXT STEPS
  • Study the Boltzmann distribution in detail, focusing on its application to quantum gases
  • Explore the derivation of energy levels for hydrogen atoms using the Rydberg formula
  • Learn about the implications of degrees of freedom in monatomic versus diatomic gases
  • Investigate temperature calculations in statistical mechanics, particularly for ideal gases
USEFUL FOR

Students of physics, particularly those studying thermodynamics and quantum mechanics, as well as educators seeking to clarify concepts related to gas behavior and energy states.

captainjack2000
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Homework Statement


A gas of hydrogen atoms has a fraction of atoms found in the n=2 quantum state of 0.05. What is the temperature of the gas?


The Attempt at a Solution


I think the gas molecules have an energy E=5/2kT (rather than E=kT ?? because diatomic gases have 5 degrees of freedom?)

E=Ry(1/n^2)?

not sure how to continue
 
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Since the question indicates these are hydrogen atoms, it is not considered a diatomic gas in this case.

Try looking up Boltzmann Factors in your textbook.
 
So the Boltzmann factor is
exp(-E/kT)=0.05

I still don't understand what you would take as the energy of the gas. It can't have a factor of kT because then the T would cancel...
 

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