Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Question
Chapter 37, Problem 36P
To determine
The frequency of vibration for HF molecule.
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The effective spring constant describing the potential energy of the HBr molecule is 410 N/m and that for the NO molecule is 1530 N/m.
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Chapter 37 Solutions
Physics for Scientists and Engineers
Ch. 37 - Prob. 1PCh. 37 - Prob. 2PCh. 37 - Prob. 3PCh. 37 - Prob. 4PCh. 37 - Prob. 5PCh. 37 - Prob. 6PCh. 37 - Prob. 7PCh. 37 - Prob. 8PCh. 37 - Prob. 9PCh. 37 - Prob. 10P
Ch. 37 - Prob. 11PCh. 37 - Prob. 12PCh. 37 - Prob. 13PCh. 37 - Prob. 14PCh. 37 - Prob. 15PCh. 37 - Prob. 16PCh. 37 - Prob. 17PCh. 37 - Prob. 18PCh. 37 - Prob. 19PCh. 37 - Prob. 20PCh. 37 - Prob. 21PCh. 37 - Prob. 22PCh. 37 - Prob. 23PCh. 37 - Prob. 24PCh. 37 - Prob. 25PCh. 37 - Prob. 26PCh. 37 - Prob. 27PCh. 37 - Prob. 28PCh. 37 - Prob. 29PCh. 37 - Prob. 30PCh. 37 - Prob. 31PCh. 37 - Prob. 32PCh. 37 - Prob. 33PCh. 37 - Prob. 34PCh. 37 - Prob. 35PCh. 37 - Prob. 36PCh. 37 - Prob. 37PCh. 37 - Prob. 38PCh. 37 - Prob. 39PCh. 37 - Prob. 40PCh. 37 - Prob. 41PCh. 37 - Prob. 42PCh. 37 - Prob. 43P
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- Air is 21% oxygen. You measure the total translational kinetic energy of the molecules of oxygen in a container to be 75J at room temperature, what is the total vibrational energy of these molecules were they at a higher temperature?arrow_forwardAssuming that the vibrations of a 14N2 molecule are equivalent to those of a harmonic oscillator with a force constant kf = 2293.8 N m−1, what is the zero-point energy of vibration of this molecule? Use m(14N) = 14.0031 mu.arrow_forwardVibrations 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]arrow_forward
- The number of normal modes of vibration depends on the shape of the molecule, but not on the number of atoms in the molecule. True Falsearrow_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_forwardWhat is the minimum energy required to go from one vibrational state to the next higher vibrational state for a molecule whose vibrations are modeled by a harmonic oscillator?arrow_forward
- The vibrational motion of H2 can be described as a harmonic oscillator with v = 4401.21 cm^-1. Calculate the fraction of molecules that have an energy equal to (3hv/2) at 1000 K Select one: 0.998 0.985 0.0018 0.0250arrow_forwardA gas phase H19F molecule has a bond length of 91.68 pm and a vibrational force constant,k = 966 N/m. For the v = 0, J = 10 and v = 1, J = 10 rovibrational levels, calculate the period of rotation andvibration. How many times does the molecule rotate during one vibrational period?arrow_forwardThe v = 0 to v = 1 vibrational transition of the HI molecule occurs at a frequency of 6.69 × 1013 Hz. The same transition for the NO molecule occurs at a frequency of 5.63 × 1013 Hz. Calculate (a) the effective force constant and (b) the amplitude of vibration for each molecule. (c) Explain why the force constant of the NO molecule is so much larger than that of the HI molecule.arrow_forward
- Consider the 1-dimensional linear chain in the Figure 5 below with N atoms in the chain. How many vibrational branches will be in the dispersion relation ?arrow_forwardThe 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_forwardConsider a Face Centered Cubic (FCC) lattice structured Nickel crystal. We are looking to find the surface energy of the new surface that is formed after it is sliced at the (100) plane. a- Find the value of R as function of the lattice constant a. 4R Oa = 2R Oa = 4R Oa = = 2/2R V2 Find the area A11 of (111) surface as function of R. 04R? O16R? O8R? OR? How many atoms lie on the plane (111) within the unit cell? N111 = atoms within the unit cell Find the number of atoms per unit surface area. 2 2 R2 8R2 16R? 4R? Which of the following represents the expression of the surface energt? ON BEPAarrow_forward
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