Chapter 18, Problem 18.9E

Interpretation Introduction

Interpretation:

The values of $q_{\text{elect}}$ for $\text{Ni}$ atoms at $298\text{K}$ and $q_{\text{elect}}$ for $\text{Ni}$ atoms at $1000\text{K}$ are to be compared. Whether an explanation as to why the answers are so close could be predicted or not is to be stated. The values of $q_{\text{elect}}$ for $\text{Ni}$ atoms at $5\text{K}$ and $q_{\text{elect}}$ at $298\text{K}$ are to be compared. The explanation for corresponding different answers could be predicted or not is to be stated.

Concept introduction:

Different linearly independent wavefunctions that have same energy are called degenerate. This is expressed in terms of degeneracy. If two functions are having same energy then they are called doubly degenerate and so on. The electronic partition function is represented as,

$q_{\text{elect}}={\displaystyle \sum _i{g}_i{e}^{-{\in }_i/\text{kT}}}$

Where,

• $g_i$ represents the degeneracy.

• ${\in }_i$ represents the energy of $i^{th}$ microstate.

• $k$ represents the Boltzmann constant with value $1.381\times {10}^{-23}\text{J}/\text{K}$.

• $T$ represents the temperature $\left(\text{K}\right)$.