Please do it step by step because I really want to understand the HW?? 3. Vibrational excitations in a diatomic molecule can be described with a potentialenergy function of the formU (r) = D(e-2a(r-re) – 2e¬a(r-re))where r is the interatomic distance, re is the equilibrium bond distance, D is thedissociation energy (a constant), and a is a positive constant.a) What are the dimensions of re, D, and a? Express your answer in terms ofproducts LªT'M°, where L is length, T is time, M is mass, and a, b, and c arerational numbers.b) What is the value of the potential at arbitrarely large separations (r > re).c) Find the value of r for which U is a minimum.d) What is the minimum value of U?e) Show that for very small displacements x =ergy can be approximated to(r – re) << 1, the potential en-U (x) – U (0)kawhere k2a? D.

Since you have asked multipart question. So, I have answered first 4 parts. If you need the answer…

3. Vibrational excitations in a diatomic molecule can be described with a potential energy function of the form U(r) = D(e-2a(r-re) – 2e¬a(r-re)) %3D where r is the interatomic distance, re is the equilibrium bond distance, D is the dissociation energy (a constant), and a is a positive constant.

3. Vibrational excitations in a diatomic molecule can be described with a potential energy function of the form U(r) = D(e-2a(r-re) – 2e¬a(r-re)) %3D where r is the interatomic distance, re is the equilibrium bond distance, D is the dissociation energy (a constant), and a is a positive constant.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

a) Calculate the characteristic temperature associated with a vibrational energy level transition of angular frequency ω = 2×1013 rad s-1 . b). A process “freezes out” at temperatures below 42 K. Calculate the typical energy associated with this process.
Set up the relevant equations with estimates of all missing parameters. The molecular bond (spring constant) of HCl is about 470 N/m. The moment of incrtia is 2.3 x 10-47 kg-m². (a) At 300 K what is the probability that the molecule is in its lowest excited vibrational state? (c) Of the molecules in the vibrational ground state what is the ratio of the number in the gronnd rotational state to the number in the first excited rotational state?
The parameters o and & in Lennard-Jones potential in Argon (Ar) crystals are o = 3.40 x 10-10 m and ɛ = 1.67 x 10-21 J. The lattice sums for the BCC (body-centered cubic) structures are E C" Pī12 = 9.11418, ECC Pī = 12.2533, and the lattice sums for the FCC structures are 2CC Pī12 = potential, calculate the equilibrium separation and cohesive energies (in unit of electron voltage or eV) for BCC and FCC configurations. -6 %3| 12.13188, ECC Pi = 14.45392. Using the Lennard-Jones %3D
The force constant of the Cl2 molecule is 323 Nm-1. Calculate the energy at the zero point of vibration and if this amount of energy is converted to translational energy, how fast would the molecule be moving?
c) Let's think about this. To a first approximation, a diatomic molecule can be represented by a harmonic oscillator. However, we learned that the Morse oscillator provides a better representation of a diatomic molecule. The figure below shows the harmonic and Morse potential energy curves for a diatomic molecule, along with corresponding vibrational wavefunctions. How do you expect the average bond length of a diatomic molecule would change if the molecule transitions from the ground to any of the excited vibrational levels when: 1) the molecule is represented by the harmonic potential, and 2) the molecule is represented by the Morse potential? Explain your reasoning. Harmonic potential Morse potential Vs V4 Vs V1 Vo vo Reg Reg
o atom2) The interatomic interaction energy for two atoms (with masses m₁ and m2) of a diatomic molecule is given as: A B Eint. (r) 12 r oms(A where r is the distance between these two atoms (A and B are positive con-troni (bondstants) Find the binding energy, equilibrium (bond) distance between two ilc in teratoms and vibrational frequency of the molecule in terms of given parameters.
M Inbox (44,3 x w Virginia Cor X Frcc Chapter 4 H x Visual session.masteringphysics.com/myct/itemView?assig Apps Getting Started Thomson Reuters o ADP ezLaborManag Ch 07 HW Exercise 7.35 - Enhanced - with Feedback The potential energy of two atoms in a diatomic molecule is approximated by U (r) = a/r-b/r°, where r is the spacing between atoms and a and b are positive constants.
a) Consider a plane in a body-centered cubic lattice where a = 4.225 Å. State the Miller indices and the direction vector of this plane. b) What is the distance between adjacent planes in this cubic crystal?
Question 1 Simple Cubic Lattice, Part 1 Consider a simple cubic (sc) crystal in which one atom is placed at each lattice point. The lattice constant is a = 0.7\: nma=0.7nm. Calculate the volume density of atoms (i.e. number of atoms per unit volume) in unit of cm^{-3}cm−3. Values within 5% error will be considered correct.
1. A model for the potential energy interaction between the two nitrogen atoms in the N2 molecule is proposed that has the form: v(4) = 4E, (4)* - ()'] 12 a. Find the position of the potential minimum and its value there, in terms of o and Eo, respectively. What do these parameters represent physically about the molecule? b. Draw a hand sketch of V(r) showing rmin, V(rmin) and where V crosses the r axis. c. If the atom is disturbed from its equilibrium by a small amount, show that the 7.56. frequency of oscillation is w = d. For molecular nitrogen, the bond length is 1.1 x 10-1°m, the bond (binding) energy is 9.79 eV (15.66 x 10-19 J), the mass is 14 amu = 23.38 x 10-27 kg. In the spectroscopy laboratory, this vibration is measured to be 8.8 x 1013 Hz. Is this a good model for the interatomic potential? (Recall o = 2n times frequency in Hz) where m is the mass of a nitrogen atom.
8. The vibrational constant o for O2 molecule is 1580 cm. Calculate the maximum displacement (r - re) in Å as a percentage of r. (= 1-207 Ả), when v = 0, v = 15. Assume that the molecule is a harmonic oscillator and r, is the %3D eauilibrium internuclear distance. CS Scanned with CamScanner
Hcp structure. Show that the c/a ratio for an ideal hexagonal closed-packed structure is () = 1.633. If c/a is significantly larger than this value, the crystal structure may be thought of as composed of planes of closely packed atoms, the planes being loosely stacked.