Vibration energy levels are evenly spaced. Calculate the vibrational partition function at 500.0 K for a...
Vibration energy levels are evenly spaced. Calculate the vibrational partition function at 500.0 K for a diatomic molecule whose εvibrational is 1.19e-20 J. What fraction of the molecules would have vibrational energy 1ε=1.19e-20 J?
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Vibration energy levels are evenly spaced. Calculate the
vibrational partition function at 500.0 K for a...
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...
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....
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)...
2. There is a system with infinite evenly spaced energy levels, with the ground state at true zer...
Need ASAP
2. There is a system with infinite evenly spaced energy levels, with the ground state at true zero. The spacing is cquivalent to 100cm-1. The levels are doubly degenerate in the ground state, then singly degenerate, then doubly degenerate, etc. (Please see the figure.) The partition function can be found both numerically and analytically. At 27C, how many levels must be included in a summation to ensure numerical accuracy to 10%? How many levels must be included in...
Write down an expression for calculating the vibrational partition function for a polyatomic mole...
Write down an expression for calculating the vibrational partition function for a polyatomic molecule from the vibrational partition functions of its normal modes. Use the spectroscopic data below to calculate qvib for carbon dioxide and ozone at 300 K. 4 Molecule Carbon dioxide, CO2 13 Ozone, O3 Vi/cm v2/ cm-1 667 701 V3 / cm-1 2349 1042 1103
Write down an expression for calculating the vibrational partition function for a polyatomic molecule from the vibrational partition functions of its normal...
6. Consider the bond vibration of a homo-atomic diatomic molecule. In the harmonic approximation the vibrational...
6. Consider the bond vibration of a homo-atomic diatomic molecule. In the harmonic approximation the vibrational energy levels are given by, Where v = 0,1,..., and w = 6.1 x 1014 5-1. Let us assume this vibrational mode is IR active. A photon of energy E = hc/, is absorbed by the molecule and induces a fundamental vibrational transition. (a) What is the wavelength of the resulting IR absorption peak in nm? [6 marks] (b) Is it reasonable to assume...
You are studying a system that has five evenly spaced energy levels. The lowest energy level (lab...
You are studying a system that has five evenly spaced energy levels. The lowest energy level (labeled "1") has an energy of 0.5 J. The remaining energy levels (labeled 2-5 in increasing energy) are evenly spaced, with 1 J energy spacing between the levels There are three particles in the system, and any number of particles can occupy each of the energy levels. If the average energy per particle is 3.5 J, as in the four questions above, how can...
You have in your posession the first vibrational spectrum of a new diatomic molecule X_2 obtained...
You have in your posession the first vibrational spectrum of a new diatomic molecule X_2 obtained at 1000 K. From the spectrum you determine that the fraction of molecules occupying a given vibrational energy state n is as follows: What are the vibrational energy spacings for X_2?
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...
II. (30 pts) The diatomic molecule CO has a vibrational wavenumber of 2170 cm 'and may...
II. (30 pts) The diatomic molecule CO has a vibrational wavenumber of 2170 cm 'and may be treated as a quantized harmonic oscillator. 1. (10 pts) What is the energy of one photon of light which has the same frequency as CO (in J units)? 2. (10 pts) What is the value of the vibrational partition function of CO at 300 K? 3. (10 pts) At what temperature would approximately 5 vibrational quantum states of Co be thermally populated?
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...
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....
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)...
Need ASAP
2. There is a system with infinite evenly spaced energy levels, with the ground state at true zero. The spacing is cquivalent to 100cm-1. The levels are doubly degenerate in the ground state, then singly degenerate, then doubly degenerate, etc. (Please see the figure.) The partition function can be found both numerically and analytically. At 27C, how many levels must be included in a summation to ensure numerical accuracy to 10%? How many levels must be included in...
Write down an expression for calculating the vibrational partition function for a polyatomic molecule from the vibrational partition functions of its normal modes. Use the spectroscopic data below to calculate qvib for carbon dioxide and ozone at 300 K. 4 Molecule Carbon dioxide, CO2 13 Ozone, O3 Vi/cm v2/ cm-1 667 701 V3 / cm-1 2349 1042 1103
Write down an expression for calculating the vibrational partition function for a polyatomic molecule from the vibrational partition functions of its normal...
6. Consider the bond vibration of a homo-atomic diatomic molecule. In the harmonic approximation the vibrational energy levels are given by, Where v = 0,1,..., and w = 6.1 x 1014 5-1. Let us assume this vibrational mode is IR active. A photon of energy E = hc/, is absorbed by the molecule and induces a fundamental vibrational transition. (a) What is the wavelength of the resulting IR absorption peak in nm? [6 marks] (b) Is it reasonable to assume...
You are studying a system that has five evenly spaced energy levels. The lowest energy level (labeled "1") has an energy of 0.5 J. The remaining energy levels (labeled 2-5 in increasing energy) are evenly spaced, with 1 J energy spacing between the levels There are three particles in the system, and any number of particles can occupy each of the energy levels. If the average energy per particle is 3.5 J, as in the four questions above, how can...
You have in your posession the first vibrational spectrum of a new diatomic molecule X_2 obtained at 1000 K. From the spectrum you determine that the fraction of molecules occupying a given vibrational energy state n is as follows: What are the vibrational energy spacings for X_2?
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...
II. (30 pts) The diatomic molecule CO has a vibrational wavenumber of 2170 cm 'and may be treated as a quantized harmonic oscillator. 1. (10 pts) What is the energy of one photon of light which has the same frequency as CO (in J units)? 2. (10 pts) What is the value of the vibrational partition function of CO at 300 K? 3. (10 pts) At what temperature would approximately 5 vibrational quantum states of Co be thermally populated?
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