PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
6th Edition
ISBN: 9781429206099
Author: Tipler
Publisher: MAC HIGHER
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Chapter 35, Problem 4P
To determine
The value of force constant for entire spring.
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Atoms vibrate relative to one another in molecules with the bond acting as a spring.
Consider the H – CI bond, where the heavy Cl atom forms a stationary anchor for the very
light H atom. That is, only the H atom moves, vibrating as a simple harmonic oscillator.
(a) Give the equation that describes the allowed vibrational energy levels of the bond.
(b) The force constant kf for the H – Cl bond is 516.3 N m'1. Given the mass of H equal to
1.7 x 1027 kg, determine the difference in energy (separation) between adjacent energy
levels.
(c) Calculate the zero-point energy of this molecular oscillator.
V7
What 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?
Chapter 35 Solutions
PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
Ch. 35 - Prob. 1PCh. 35 - Prob. 2PCh. 35 - Prob. 3PCh. 35 - Prob. 4PCh. 35 - Prob. 5PCh. 35 - Prob. 6PCh. 35 - Prob. 7PCh. 35 - Prob. 8PCh. 35 - Prob. 9PCh. 35 - Prob. 10P
Ch. 35 - Prob. 11PCh. 35 - Prob. 12PCh. 35 - Prob. 13PCh. 35 - Prob. 14PCh. 35 - Prob. 15PCh. 35 - Prob. 16PCh. 35 - Prob. 17PCh. 35 - Prob. 18PCh. 35 - Prob. 19PCh. 35 - Prob. 20PCh. 35 - Prob. 21PCh. 35 - Prob. 22PCh. 35 - Prob. 23PCh. 35 - Prob. 24PCh. 35 - Prob. 25PCh. 35 - Prob. 26PCh. 35 - Prob. 27PCh. 35 - Prob. 28PCh. 35 - Prob. 29PCh. 35 - Prob. 30PCh. 35 - Prob. 31PCh. 35 - Prob. 32PCh. 35 - Prob. 33PCh. 35 - Prob. 34PCh. 35 - Prob. 35PCh. 35 - Prob. 36PCh. 35 - Prob. 37PCh. 35 - Prob. 38P
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- The greenhouse-gas carbon dioxide molecule CO2 strongly absorbs infrared radiation when its vibrational normal modes are excited by light at the normal-mode frequencies. CO₂ is a linear triatomic molecule, as shown in (Figure 1), with oxygen atoms of mass mo bonded to a central carbon atom of mass mc. You know from chemistry that the atomic masses of carbon and oxygen are, respectively, 12 and 16. Assume that the bond is an ideal spring with spring constant k. There are two normal modes of this system for which oscillations take place along the axis. (You can ignore additional bending modes.) In this problem, you will find the normal modes and then use experimental data to determine the bond spring constant. Figure O 1 mo 1x₁ 2 mc 1 of 1 3 mo 1Xz Part A Let x₁, x2, and 3 be the atoms' positions measured from their equilibrium positions. First, use Hooke's law to write the net force on each atom. Pay close attention to signs! For each oxygen, the net force equals mod²x/dt². Carbon has a…arrow_forwardAir 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_forwardMolecular Pair Potential The vibrational properties of a diatomic molecule can often be described by Mie's pair potential 3: U(r) = C c[9₁-9] (4) where U(r) is the potential energy between the two atoms, r is the distance between the two atoms, C, o are positive constants, and λ > 6 is a constant. The case with X 12 is the Lennard-Jones potential and was covered in Lecture #2. For the purposes of this problem, assume there is a mass ‘m’ that represents the dynamical mass of the molecule. 4 TLTR: (a) Find a combination of C, m, o that has the units of frequency. (b) Derive the ratio of the equilibrium positions and of the frequencies of small oscillations for X 10, 14. Show that the units for the equilibrium position and for the frequency of the oscillations are consistent.arrow_forward
- Solid state physics question: Plot a dispersion curve for longitudinal vibrations in a 1D crystal with a basis of two atoms at each lattice point. Justify the values you used to generate the curve.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_forwardThe diatomic radical, 160¹H, can be treated approximately as a harmonic oscillator, with a force constant of 780.7 N/m, mH = 1.007825 Dalton, and mo = 15.9949146 Dalton. (a) What is the harmonic angular frequency, w, of this oscillator (in sec¯¹)? (b) Spectroscopic measurements are often used to characterize molecular oscillators, and in doing so, they relate a wavelength of light to its characteristic oscillation frequency through the relation, w = 2πc. Use this to find in units of cm-1 (wavenumbers). λ = (c) If the force constant is the same, what would be in wavenumbers (cm-¹) for ¹60 ²H (²H = deuterium), with mH = 2.014101778 Dalton?arrow_forward
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