Consider a molecule that has two energy levels separated by e, where the ground state has...
Consider a molecule that has two energy levels separated by e, where the ground state has a degeneracy of 2 and the excited state has a degeneracy of 3. (a) What is the expression for the partition function at temperature T? (b) What are the fractional populations of the two states at temperature T? (c) What is the internal energy per particle at temperature T?
Homework Answers
Add Answer to:
Consider a molecule that has two energy levels separated by e,
where the ground state has...
An atom in a solid has two energy levels: a ground state of degeneracy g_1 and...
An atom in a solid has two energy levels: a ground state of degeneracy g_1 and an excited state of degeneracy g_2 at an energy Delta above the ground state. Show that the partition function atom is Z_atom is Z_atom = g_1 + g_2 e^-beta Delta. (a) Show that the heat capacity of the atom is given by C = g_1 g_2 Delta^2 e^-beta Delta/k_B T^2 (g_1 + g_2 e^-beta Delta)^2. A monatomic gas of such atoms has a partition...
Huckel/PIB a) Calculate the ground-state energy levels of the π-network in hexatriene, model, and for each...
Huckel/PIB
a) Calculate the ground-state energy levels of the π-network in hexatriene, model, and for each of them indicate the associated degeneracy. To ca molecule is linear and use the values 135 and 154 pm for C-C and C-C bonds CoHs, using the particle in the box lculate the box length, assume that the to induce a transition from the ground state to the first excited e can be obtained using Huckel theory. Knowing b) What is the wavelength of...
3. Consider a canonical system with uniformly spaced energy levels (spacing = e). The populations of...
3. Consider a canonical system with uniformly spaced energy levels (spacing = e). The populations of the energy levels are given by the Bolzmann distribution (a) What fraction of particles is in the ground state at T 300 K when the energy spacing is e 3.0 x 10-20 J? You can set the ground state energy to be zero. (b) The e value mentioned in part (a) is the typical energy spacing in the vibrational energy levels of a molecule....
3. Consider a canonical system with uniformly spaced energy levels (spacing = €). The populations of...
3. Consider a canonical system with uniformly spaced energy levels (spacing = €). The populations of the energy levels are given by the Bolzmann distribution. (a) What fraction of particles is in the ground state at T = 300 K when the energy spacing is € = 3.0 x 10-20 J? You can set the ground state energy to be zero. (b) The e value mentioned in part (a) is the typical energy spacing in the vibrational energy levels of...
hc 3 (25pt) Consider a set of n energy levels that are evenly-spaced by energy and that each level is n-fold degenerate. The degeneracy of the energy levels allows us to write the molecular parti...
hc 3 (25pt) Consider a set of n energy levels that are evenly-spaced by energy and that each level is n-fold degenerate. The degeneracy of the energy levels allows us to write the molecular partition function as: a. Approximate this sum by an integral and find an analytical form of the partition function. b. Calculate the partition function at 298 K given that A -100 microns. c. Find the contribution to internal energy from statistical mechanical expression,
hc 3 (25pt)...
Question 5 The rotational energy levels of a diatomic molecule are given by E,= BJ(J+1) with...
Question 5 The rotational energy levels of a diatomic molecule are given by E,= BJ(J+1) with B the rotational constant equal to 8.02 cm Each level is (2) +1)-times degenerate. (wavenumber units) in the present case (a) Calculate the energy (in wavenumber units) and the statistical weight (degeneracy) of the levels with J =0,1,2. Sketch your results on an energy level diagram. (4 marks) (b) The characteristic rotational temperature is defined as where k, is the Boltzmann constant. Calculate the...
A system consists of two non-degenerate states separated in energy by an amount e As the...
A system consists of two non-degenerate states separated in energy by an amount e As the temperature is raised towards infinity, which of the following statements is correct? A. The frequency of photons whose energy matches the transition energy goes do B. The population in the upper state will exceed that in the ground state. C. The probability of a molecule occupying either state becomes similar D. At a sufficiently high temperature laser action will occur. Ground state Br2 dissociates...
Consider a simple single quantum particle with the energy levels of the harmonic oscillator En =...
Consider a simple single quantum particle with the energy levels of the harmonic oscillator En = (n + 1/2)ℏω. This particle is in thermal contact with a reservoir with temperature T. a) Calculate the partition function of this particle. b) Calculate the internal energy of the particle as a function of temperature. Deduce and interpret the state of this energy at low and high temperatures. c) Calculate the specific temperature of this particle at constant pressure.
Question 9 Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle...
Question 9 Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle energy levels, with energies 81 0, 82 2 and E3 38.The system is in thermal equilibrium at temperature T. (a) Suppose the particles which can occupy an energy level. are spinless, and there is no limit to the number of particles (i) How many states do you expect this system to have? Justify your answer (ii) Make a table showing, for each state of...
The NO molecule has a doubly degenerate excited electronic level 121.1cm-1 above the double degenerate electronic...
The NO molecule has a doubly degenerate excited electronic level 121.1cm-1 above the double degenerate electronic ground term. (a) Calculate the electronic partition function of NO at T=0K, T=298K and T=1000K. (b) Evaluate the populations of ground and excited states and (c) the mean electronic energy at 298K.
An atom in a solid has two energy levels: a ground state of degeneracy g_1 and an excited state of degeneracy g_2 at an energy Delta above the ground state. Show that the partition function atom is Z_atom is Z_atom = g_1 + g_2 e^-beta Delta. (a) Show that the heat capacity of the atom is given by C = g_1 g_2 Delta^2 e^-beta Delta/k_B T^2 (g_1 + g_2 e^-beta Delta)^2. A monatomic gas of such atoms has a partition...
Huckel/PIB
a) Calculate the ground-state energy levels of the π-network in hexatriene, model, and for each of them indicate the associated degeneracy. To ca molecule is linear and use the values 135 and 154 pm for C-C and C-C bonds CoHs, using the particle in the box lculate the box length, assume that the to induce a transition from the ground state to the first excited e can be obtained using Huckel theory. Knowing b) What is the wavelength of...
3. Consider a canonical system with uniformly spaced energy levels (spacing = e). The populations of the energy levels are given by the Bolzmann distribution (a) What fraction of particles is in the ground state at T 300 K when the energy spacing is e 3.0 x 10-20 J? You can set the ground state energy to be zero. (b) The e value mentioned in part (a) is the typical energy spacing in the vibrational energy levels of a molecule....
3. Consider a canonical system with uniformly spaced energy levels (spacing = €). The populations of the energy levels are given by the Bolzmann distribution. (a) What fraction of particles is in the ground state at T = 300 K when the energy spacing is € = 3.0 x 10-20 J? You can set the ground state energy to be zero. (b) The e value mentioned in part (a) is the typical energy spacing in the vibrational energy levels of...
hc 3 (25pt) Consider a set of n energy levels that are evenly-spaced by energy and that each level is n-fold degenerate. The degeneracy of the energy levels allows us to write the molecular partition function as: a. Approximate this sum by an integral and find an analytical form of the partition function. b. Calculate the partition function at 298 K given that A -100 microns. c. Find the contribution to internal energy from statistical mechanical expression,
hc 3 (25pt)...
Question 5 The rotational energy levels of a diatomic molecule are given by E,= BJ(J+1) with B the rotational constant equal to 8.02 cm Each level is (2) +1)-times degenerate. (wavenumber units) in the present case (a) Calculate the energy (in wavenumber units) and the statistical weight (degeneracy) of the levels with J =0,1,2. Sketch your results on an energy level diagram. (4 marks) (b) The characteristic rotational temperature is defined as where k, is the Boltzmann constant. Calculate the...
A system consists of two non-degenerate states separated in energy by an amount e As the temperature is raised towards infinity, which of the following statements is correct? A. The frequency of photons whose energy matches the transition energy goes do B. The population in the upper state will exceed that in the ground state. C. The probability of a molecule occupying either state becomes similar D. At a sufficiently high temperature laser action will occur. Ground state Br2 dissociates...
Question 9 Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle energy levels, with energies 81 0, 82 2 and E3 38.The system is in thermal equilibrium at temperature T. (a) Suppose the particles which can occupy an energy level. are spinless, and there is no limit to the number of particles (i) How many states do you expect this system to have? Justify your answer (ii) Make a table showing, for each state of...
Most questions answered within 3 hours.
-
Your friend is interested in the characteristics of fast tree
planters. He searched through the records...
asked 1 minute ago -
. 0.67 g of Ag is deposited electrolytically from
AgNO3 after a certain period of time...
asked 2 minutes ago -
assuming that the boric acid, h3po3 present at the end of the
borax tritation has a...
asked 1 minute ago -
When a carbonate solution is acidified, carbon dioxide is
produced.
2H+(aq) + CO32-(aq) → H2O(l) +...
asked 41 minutes ago -
A reaction has the following rate law: Rate =
kr[A][B]2. In experiment 1, the
concentrations of...
asked 38 minutes ago -
king owns a large number of public pay phones. as rhe use of
payphones decline deamatically,...
asked 42 minutes ago -
3.7 - A book is sitting on a table. The mass of the book
is 1...
asked 58 minutes ago -
Which term describes the process by which a single strand of DNA
serves as a template...
asked 1 hour ago -
LAB FOOD DRING
ANSWER THE QUESTIONS:
Q1. What value is the moisture content versus time and...
asked 1 hour ago -
You are told that an object has zero acceleration. Two forces on
the object are: F_1...
asked 1 hour ago -
The usual starting point for preparing a master budget is
forecasting or estimating:
Multiple Choice
Sales....
asked 1 hour ago -
How to make a simple game in pygame where an object is randomly
falling from the...
asked 1 hour ago