Homework Answers
For an harmonic oscillator the restoring force is directly proportional to equillibirium displacement (distance from fix point) but the exat form is anharmonic oscillator because the molecule is not rigid completely and due to fro and back motion the bond length get extended more due to repeating process , it happens naturally.
Hence anharmonic oscillaor is exact model than harmonic oscillator.
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5. We have used the harmonic oscillator and rigid rotator as approximations for the vibrational a...
a) Describe and sketch the vibrational energy levels observed for diatomic molecules in the harmonic oscillator...
a) Describe and sketch the vibrational energy levels observed for diatomic molecules in the harmonic oscillator approximation, using an appropriate formula to support your answer (4 marks) b) State the selection rules for IR transitions in diatomic molecules. (2 marks) c) Briefly explain the implications of anharmonicity for vibrational spectra, with particular reference to the selection rules for diatomic molecules, and the resultant energy levels and spectra observed. (3 marks)
a) Describe and sketch the vibrational energy levels observed for...
a. Sketch the expected shape of the pure vibrational absorption spectrum of a diatomic molecule that...
a. Sketch the expected shape of the pure vibrational absorption spectrum of a diatomic molecule that is well described by the harmonic oscillator model (absorbance as a function of frequency). (We are pretending that there are no rotations occurring for this question. For real diatomic molecules, if they are IR active, there will also be rotational excitations and therefore a rovibrational spectrum.) In what portion of the electromagnetic radiation spectrum would you expect this absorption to occur? b. Sketch the...
2. The vibrational frequency of gaseous N O is 1904 cm. Assume this molecule is a harmonic oscillator 2.1 What is the energy of the electromagnetic wave corresponding to this vibrational frequenc...
2. The vibrational frequency of gaseous N O is 1904 cm. Assume this molecule is a harmonic oscillator 2.1 What is the energy of the electromagnetic wave corresponding to this vibrational frequency? 2.2 Calculate the force constant of "NO 2.3 Calculate the vibrational frequency of gaseous N O. The isotopic effect does not change the force constant of the harmonic oscillator. 2.4 When "N'O is bound to hemoglobin A (Hb or Hgb, the iron-containing oxygen-transport metalloprotein in the red blood...
Explain (in your own chemically accurate words) why and how you can use IR spectroscopy to...
Explain (in your own chemically accurate words) why and how you can use IR spectroscopy to measure bonding parameters for a polar, diatomic molecule. You will need to address why the ro-vibrational spectrum is in the IR region of the electromagnetic spectrum (this may include a discussion of vibrational and rotational motion and the selection rules associated with them) the origin of the P, Q and R branch (including a figure to indicate the origin of each set of peaks...
question no 4.22, statistical physics by Reif Volume 5 4.92 Mean energy of a harmonic oscillator A harmonic oscillator...
question no 4.22, statistical physics by Reif Volume 5
4.92 Mean energy of a harmonic oscillator A harmonic oscillator has a mass and spring constant which are such that its classical angular frequency of oscllation is equal to w. In a quantum- mechanical description, such an oscillator is characterized by a set of discrete states having energies En given by The quantum number n which labels these states can here assume all the integral values A particular instance of a...
2. [10 points] For a Simple Harmonic Oscillator: a) Draw ψ(x) and ψ2(x) for the u,...
2. [10 points] For a Simple Harmonic Oscillator: a) Draw ψ(x) and ψ2(x) for the u, and v-6 states. Make sure to include as much detail as possible. b) Show that 2(3) is normalized. 3. [5] A certain non-halogen diatomic molecule was found to have a force constant of 99 N/m and an observed vibrational frequency of 162.2 cm1 Determine the identity of the unknown diatomic 4. [10 points) a) What is the difference between commuting and non-commuting operators? What...
8.4 The Two-Dimensional Central-Force Problem The 2D harmonic oscillator is a 2D central force pr...
8.4 The Two-Dimensional Central-Force Problem The 2D harmonic oscillator is a 2D central force problem (as discussed in TZD Many physical systems involve a particle that moves under the influence of a central force; that is, a force that always points exactly toward, or away from, a force center O. In classical mechanics a famous example of a central force is the force of the sun on a planet. In atomic physics the most obvious example is the hydrogen atom,...
1. (30pt) LC Circuit and Simple Harmonic Oscillator (From $23.12 RLC Series AC Circuits) Let us...
1. (30pt) LC Circuit and Simple Harmonic Oscillator (From $23.12 RLC Series AC Circuits) Let us first consider a point mass m > 0 with a spring k> 0 (see Figure 23.52). This system is sometimes called a simple harmonic oscillator. The equation of motion (EMI) is given by ma= -kr (1) where the acceleration a is given by the second derivative of the coordinate r with respect to time t, namely dr(t) (2) dt de(t) (6) at) (3) dt...
1. Consider a dilute solution of molecules at fixed temperature T. These molecules have access to...
1. Consider a dilute solution of molecules at fixed temperature T. These molecules have access to a surface that has a total of B binding sites where molecules can bind. To count states in this system, we will divide space into small cells that each can hold a single molecule. There are a total of B cells that have a binding site, and a total of M cells that do not have binding sites. The overall number of cells is...
(a) What is Hückel theory? Why is it used? What assumptions does it make? (b) Consider...
(a) What is Hückel theory? Why is it used? What assumptions does it make? (b) Consider hexatriene, how many molecular orbitals would you expect there to be? (C) Write the secular determinant for the hexatriene system. (d) Using Hückel approximations, re-write the Hückel secular determinant using the appropriate variables, and explain what the variable represent. (e) Determine the energies of the molecular orbitals (1) Determine the total energy of the -electronic energy in hexatriene (9) Hückel theory is meant as...
a) Describe and sketch the vibrational energy levels observed for diatomic molecules in the harmonic oscillator approximation, using an appropriate formula to support your answer (4 marks) b) State the selection rules for IR transitions in diatomic molecules. (2 marks) c) Briefly explain the implications of anharmonicity for vibrational spectra, with particular reference to the selection rules for diatomic molecules, and the resultant energy levels and spectra observed. (3 marks)
a) Describe and sketch the vibrational energy levels observed for...
2. The vibrational frequency of gaseous N O is 1904 cm. Assume this molecule is a harmonic oscillator 2.1 What is the energy of the electromagnetic wave corresponding to this vibrational frequency? 2.2 Calculate the force constant of "NO 2.3 Calculate the vibrational frequency of gaseous N O. The isotopic effect does not change the force constant of the harmonic oscillator. 2.4 When "N'O is bound to hemoglobin A (Hb or Hgb, the iron-containing oxygen-transport metalloprotein in the red blood...
question no 4.22, statistical physics by Reif Volume 5
4.92 Mean energy of a harmonic oscillator A harmonic oscillator has a mass and spring constant which are such that its classical angular frequency of oscllation is equal to w. In a quantum- mechanical description, such an oscillator is characterized by a set of discrete states having energies En given by The quantum number n which labels these states can here assume all the integral values A particular instance of a...
2. [10 points] For a Simple Harmonic Oscillator: a) Draw ψ(x) and ψ2(x) for the u, and v-6 states. Make sure to include as much detail as possible. b) Show that 2(3) is normalized. 3. [5] A certain non-halogen diatomic molecule was found to have a force constant of 99 N/m and an observed vibrational frequency of 162.2 cm1 Determine the identity of the unknown diatomic 4. [10 points) a) What is the difference between commuting and non-commuting operators? What...
8.4 The Two-Dimensional Central-Force Problem The 2D harmonic oscillator is a 2D central force problem (as discussed in TZD Many physical systems involve a particle that moves under the influence of a central force; that is, a force that always points exactly toward, or away from, a force center O. In classical mechanics a famous example of a central force is the force of the sun on a planet. In atomic physics the most obvious example is the hydrogen atom,...
1. (30pt) LC Circuit and Simple Harmonic Oscillator (From $23.12 RLC Series AC Circuits) Let us first consider a point mass m > 0 with a spring k> 0 (see Figure 23.52). This system is sometimes called a simple harmonic oscillator. The equation of motion (EMI) is given by ma= -kr (1) where the acceleration a is given by the second derivative of the coordinate r with respect to time t, namely dr(t) (2) dt de(t) (6) at) (3) dt...
1. Consider a dilute solution of molecules at fixed temperature T. These molecules have access to a surface that has a total of B binding sites where molecules can bind. To count states in this system, we will divide space into small cells that each can hold a single molecule. There are a total of B cells that have a binding site, and a total of M cells that do not have binding sites. The overall number of cells is...
(a) What is Hückel theory? Why is it used? What assumptions does it make? (b) Consider hexatriene, how many molecular orbitals would you expect there to be? (C) Write the secular determinant for the hexatriene system. (d) Using Hückel approximations, re-write the Hückel secular determinant using the appropriate variables, and explain what the variable represent. (e) Determine the energies of the molecular orbitals (1) Determine the total energy of the -electronic energy in hexatriene (9) Hückel theory is meant as...
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