Bundle: Physics For Scientists And Engineers With Modern Physics, Loose-leaf Version, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Single-term
10th Edition
ISBN: 9781337888585
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Question
Chapter 42, Problem 9P
(a)
To determine
The minimum amplitude of vibration of HI molecule.
(b)
To determine
The minimum amplitude of vibration of HF molecule.
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The frequency of the photon that causes the υ = 0 to υ = 1 transition in the CO molecule is 6.42 x 1013 Hz. We ignore any changes in the rotational energy for this example.(A) Calculate the force constant k for this molecule. (B) What is the classical amplitude A of vibration for this molecule in the υ = 0 vibrational state?
Vibrations in the diatomic molecule CO can be approximated as
a harmonic oscillator, where the angular frequency
w = 6.505 × 1013 Hz and the reduced mass is equal to
u = 1.14 × 10-27 kg. Assume the molecule is in its first
excited vibrational state. Its vibrational wavefunction can then
be written as V1 (æ) = (÷)i /2a xe-T where a =
2α πe
If
we were to measure the bond length of the molecule, what is
the most likely displacement from the equilibrium bond distance
in the first excited vibrational state? Give your answer in
Angstroms [Note: The equilibrium displacement in the Quantum
harmonic oscillator corresponds to x =
= 0, ie the coordinate x
measures displacement from equilibrium]
(b): the potential energy of a diatomic molecule is given by U =
B
where A and B are constants and r is the separation
A
r12
r6
distance between the atoms. For the H2 molecule, take A = 0.124
x 10-120 eV. m² and B = 1.488 × 10-60 eV . m°. Find the
separation distance at which the energy of the molecule is a
%3D
minimum.
Chapter 42 Solutions
Bundle: Physics For Scientists And Engineers With Modern Physics, Loose-leaf Version, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Single-term
Ch. 42.1 - For each of the following atoms or molecules,...Ch. 42.2 - Prob. 42.2QQCh. 42.2 - Prob. 42.3QQCh. 42 - Prob. 1PCh. 42 - Prob. 2PCh. 42 - Prob. 3PCh. 42 - Prob. 4PCh. 42 - Prob. 5PCh. 42 - The photon frequency that would be absorbed by the...Ch. 42 - Prob. 8P
Ch. 42 - Prob. 9PCh. 42 - Prob. 10PCh. 42 - (a) In an HCl molecule, take the Cl atom to be the...Ch. 42 - Prob. 12PCh. 42 - Prob. 13PCh. 42 - Prob. 14PCh. 42 - Prob. 15PCh. 42 - Prob. 16PCh. 42 - Prob. 17PCh. 42 - Prob. 19PCh. 42 - Prob. 21PCh. 42 - Prob. 22PCh. 42 - Prob. 23PCh. 42 - Prob. 24PCh. 42 - Prob. 25PCh. 42 - Prob. 26PCh. 42 - Prob. 27PCh. 42 - Prob. 28PCh. 42 - Prob. 29PCh. 42 - Prob. 30PCh. 42 - Prob. 32PCh. 42 - Prob. 33PCh. 42 - Prob. 35PCh. 42 - Prob. 36APCh. 42 - Prob. 37APCh. 42 - Prob. 39APCh. 42 - Prob. 40APCh. 42 - As an alternative to Equation 42.1, another useful...
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- The potential energy of two atoms in a diatomic molecule is approximated by U(r) = a/r12-b/r6, where r is the spacing between atoms and a and b are positive constants. Suppose the distance between the two atoms is equal to the equilibrium distance found in part A. What minimum energy must be added to the molecule to dissociate it - that is, to separate the two atoms to an infinite distance apart? This is called the dissociation energy of the molecule. Express your answer in terms of the variables a and b. For the molecule CO, the equilibrium distance between the carbon and oxygen atoms is 1.13\times 10-10m and the dissociation energy is 1.54\times 10-18J per molecule. Find the value of the constant a. Express your answer in joules times meter in the twelth power. Find the value of the constant b. Express your answer in joules times meter in the sixth power.arrow_forwardThe 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?arrow_forwardA gas of identical diatomic molecules absorbs electromagnetic radiation over a wide range of frequencies. Molecule 1, initially in the υ = 0 vibrational state, makes a transition to the υ = 1 state. Molecule 2, initially in the υ = 2 state, makes a transition to the υ = 3 state. What is the ratio of the frequency of the photon that excited molecule 2 to that of the photon that excited molecule 1? (a) 1 (b) 2 (c) 3 (d) 4 (e) impossible to determinearrow_forward
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