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.
-
On the night of April 18, 1775, a signal was to be sent from the
Old...
asked 34 seconds from now -
Organizations may have only a few products or many products in a
product line. Consider Campbell...
asked 8 minutes ago -
could you please help me to explain the nmr splitting
integration and chemical shift and assignment...
asked 4 minutes ago -
A
29.0 cm diameter coil consists of 23 turns of cylindrical copper
wire 2.00 mm in...
asked 10 minutes ago -
(1) Write the net ionic equation for the reaction that occurs
when equal volumes of 0.191...
asked 16 minutes ago -
Q1
Two of your friends each received the results of their
first midterm exam this term....
asked 27 minutes ago -
A 0.500-kg object, suspended from an ideal spring of spring
constant 30.2 N/m, is oscillating vertically....
asked 25 minutes ago -
Please help and show work. I keep getting the wrong answers for
these problems
1. Cell...
asked 22 minutes ago -
If there is a SNP in the read with respect to the
reference genome, how would a...
asked 24 minutes ago -
Early black-and-white television sets used an electron beam to
draw a picture on the screen. The...
asked 27 minutes ago -
What is the standard error of M (denoted as
σM ) ?
Options:
The mean of...
asked 51 minutes ago -
Explain the role of n, the sample size, in determining the size
of a generated confidence...
asked 40 minutes ago