Chapter 17, Problem 17.29E

Interpretation Introduction

Interpretation:

The temperature that is necessary to have twice as many atoms in the ground state as in the first excited state is to be calculated. The temperature that is necessary to have equal populations in the ground state and the second excited state is to be calculated. The temperature that is necessary to have equal populations in the first and second excited states is to be calculated.

Concept introduction:

When energy of an atom increases, then it gets excited from lower energy state to a higher excited state. The number of atoms present in a particular energy state depends upon the temperature and energy of the state. The ratio of atoms in two states is represented as,

$\frac{N_i}{N_k}=\frac{g_i}{g_k}{e}^{-\left({\in }_i-{\in }_k\right)/\text{kT}}$

Where,

• $g_i$ represents the degeneracy of $i^{th}$ microstate.

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

• $g_k$ represents the degeneracy of $k^{th}$ microstate.

• ${\in }_k$ represents the energy of $k^{th}$ microstate.

• $k$ represents the Boltzmann constant with value $1.38\times {10}^{-23}\text{J}/\text{K}$.

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