Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
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 force constant of the Cl2 molecule is 323
Nm-1.
Calculate the energy at the zero point of
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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 =
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If
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Chapter 42 Solutions
Physics for Scientists and Engineers with Modern Physics
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 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?arrow_forward(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.arrow_forwardOne description of the potential energy of a diatomic molecule is given by the Lennard–Jones potential, U = (A)/(r12) - (B)/(r6)where A and B are constants and r is the separation distance between the atoms. For the H2 molecule, take A = 0.124 x 10-120 eV ⋅ m12 and B = 1.488 x 10-60 eV ⋅ m6. Find (a) the separation distance r0 at which the energy of the molecule is a minimum and (b) the energy E required to break up theH2 molecule.arrow_forward
- please asaparrow_forwardGiven that the fundamental vibrational frequencies of a water molecule are 1595 cm¹, 3586 cm¹, and 3725 cm-¹, calculate its zero- point vibrational energy (in J).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
- i need the answer quicklyarrow_forwardThe potential energy of a system of two atoms is given by the relation U =-A/r + B/r10 A stable molecule is formed with the release of 8 eV energy when the interatomic distance is 2.8 Å. Find A and B and the force needed to dissociate this molecule into atoms and the interatomic distance at which the dissociation occurs.arrow_forwardThe characteristic rotational energy for a diatomic molecule consisting of two idential atoms of mass 14 u (unified mass units) is 3.68 e-4 eV. Calculate the separation distance between the two atoms. Subarrow_forward
- Gggarrow_forwardThe energy of the vibrational modes of a molecule are the same as those of a (quantum) harmonic oscillator with frequency w. There is a gas of nitrogen molecules in thermodynamic equilibrium for which ħw/ks-3340 K. You may approximate the vibrational partition function with the largest two terms in it. a) What fraction of the molecules are in the ground state and what fraction in the 1st excited state of their vibrational modes at a temperature of 700 K, b) At what temperature will 5% of the molecules be in the 1st excited vibrational state?arrow_forwardIn a vibrational-rotational spectroscopy the total energy is the sum of the energies coming from the vibration and rotation (E = E + E₁). Selection rule suggests that for transition to occur Av = ±1 and Al = ±1. At room temperature, it is assumed that the lowest vibrational state is populated and the energy can only travel upwards due to lack of population of upper vibrational states thus Av = +1. What would be the energy of a line for R, P and Q-branch if a.) Al = +1, b.) Al = -1 and c.) Al = 0 respectively.arrow_forward
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