Partition Theorem Homework: Solving for the Partition Function and Energy States

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SUMMARY

The discussion focuses on solving the partition function and energy states in statistical mechanics, specifically using the formula for the partition function, defined as ##\frac{z_{i+1}}{z_i}##. The participant attempts to calculate the partition function using the equation ##z = \Sigma_{j=1}^\infty g_j e^{\frac{-(E_j - E_i)}{KT}}## with the degeneracy function ##g_j = 2(j^2)##. Despite expecting a result of 2, the participant consistently arrives at a more complex expression, ##2 + 8e^{7.8} + ...##, indicating potential confusion regarding the energy states ##E_j## and ##E_1##, particularly questioning if ##E_1 = 13.6 eV##.

PREREQUISITES
  • Understanding of statistical mechanics concepts, particularly the partition function.
  • Familiarity with the Boltzmann constant, specifically ##K = 1.38 \times 10^{-23} J/K##.
  • Knowledge of energy state calculations in quantum mechanics.
  • Ability to convert energy units from electron volts to joules (1 eV = ##1.602 \times 10^{-19} J##).
NEXT STEPS
  • Study the derivation and applications of the partition function in statistical mechanics.
  • Learn about energy state calculations and their significance in quantum mechanics.
  • Explore the implications of degeneracy in statistical distributions.
  • Review the conversion processes between different energy units, focusing on electron volts and joules.
USEFUL FOR

Students and professionals in physics, particularly those studying statistical mechanics and quantum mechanics, as well as anyone involved in calculations related to energy states and partition functions.

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Homework Statement


Screenshot (64).png


Homework Equations


Partition function = ##\frac{z_{i+1}}{z_i} ##
##z = \Sigma_{j=1}^\infty g_j e^{\frac{-(E_j - E_i)}{KT}}##
##g_j = 2(j^2)##

The Attempt at a Solution


I should get 2, but I keep getting ##2 + 8e^7.8 + ... ##
I used ##K = 1.38 \times 10^-23## and I converted electron volts to J (1eV = ##1.602 \times10^-19##J)
 
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Calpalned said:

Homework Statement


View attachment 90647

Homework Equations


Partition function = ##\frac{z_{i+1}}{z_i} ##
##z = \Sigma_{j=1}^\infty g_j e^{\frac{-(E_j - E_1)}{KT}}##
##g_j = 2(j^2)##

The Attempt at a Solution


I should get 2, but I keep getting ##2 + 8e^7.8 + ... ##
I used ##K = 1.38 \times 10^-23## and I converted electron volts to J (1eV = ##1.602 \times10^-19##J)
Actually what is ##E_j## and ##E_1##? Isn't E_1 = 13.6?
 

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