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, N i N k = g i g k e − ( ∈ i − ∈ k ) / kT Where, • g i represents the degeneracy of i t h microstate. • ∈ i represents the energy of i t h microstate. • g k represents the degeneracy of k t h microstate. • ∈ k represents the energy of k t h microstate. • k represents the Boltzmann constant with value 1.38 × 10 − 23 J / K . • T represents the temperature ( K ) .

Question

Want to see the full answer?

Answer 1

Question

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,

NiNk=gigke−(∈i−∈k)/kT

Where,

• gi represents the degeneracy of ith microstate.

• ∈i represents the energy of ith microstate.

• gk represents the degeneracy of kth microstate.

• ∈k represents the energy of kth microstate.

• k represents the Boltzmann constant with value 1.38×10−23 J/K.

• T represents the temperature (K).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

For two nondegenerate energy levels separated by an amount of energy ε/k=500.K, at what temperature will the population in the higher-energy state be 1/2 that of the lower-energy state? What temperature is required to make the populations equal?

3. Consider a 2 × 2 square lattice of spins interacting via the Ising Hamiltonian in the absence of a magnetic field: H = - ΣSi Sj, (ij) we have set J = 1. (a) Write down all the possible configurations and calculate the energy for each one of them. (b) Calculate the partition function Z, as a function of temperature, by summing over all configurations. (c) Repeat question (3a) and (3b), using periodic boundary condi- tions.

A certain atom has a doubly degenerate ground state and an upper level of four degenerate states at 450 cm−1 above the ground level. In an atomic beam study of the atoms it was observed that 30 per cent of the atoms were in the upper level, and the translational temperature of the beam was 300 K. Are the electronic states of the atoms in thermal equilibrium with the translational states? In other words, does the distribution of electronic states correspond to the same temperature as the distribution of translational states?