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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Chapter 42, Problem 39AP
To determine
The depth of the
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Consider the wave function shown below. If the linear molecule has a length L=1.6 nm, What is the value of the u(x) at the the point
indicated by the arrow for an n=1 electron? Give your answer in nm-1/2 to 2 decimal places. Do not include bond angle corrections. Do
NOT include units in your answer.
x=0
x=2/3L
x=L
Assuming that the H² molecule behaves like a harmonic oscillator with force
constant of 573 N/m. Calculate the vibrational quantum number for which the
molecule would dissociate at 4.5 eV.
The equilibrium dissociation energy of O2 is De = 4.314 ev. The basic vibration frequency of O2 is f = 1620.0 cm -1. So how much energy is actually needed to dissociate O2 molecules at n = 3 vibrational level? Give your answer in EV.
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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- Assume that the H2 molecule behaves exactly like a harmonic oscillator with a force constant of 573N/m. (a) Find the energy (in eV) of its ground and first excited vibrational states. (b) Find the vibrational quantum number that approximately corresponds to its 4.5-eV dissociation energy.arrow_forwardThe graph shows the potential energy curve for a system of two oxygen atoms. Imagine the two atoms are in a bound state. If they are 0.1 nm apart and have no kinetic energy, what is the minimum amount of energy (in Joules) that needs to be added to the system in order to break the bond?arrow_forwardA diatomic molecule begins in the vibration-rotation state characterized by n = 1, J = 7. It then absorbs a photon of light to make a R-branch transition. Which of the following represents a possible final state for this molecule? On=0,J = 7 n=2, J = 7 n = 1, J = 8 On=2, J = 8 n = 1, J = 6 n = 2, J = 6arrow_forward
- For a spherical sodium particle of 25 nm radius crystalizing in a BCC structure having a density of 1.51 g/cm^3, estimate the surface energy of the particle. b. Estimate the surface energy of {100},{110} and {111} surfaces of an FCC lattice with bond strength of 7.97 eV and lattice parameter of 4.2 Å. Also compare the energies.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_forwardIn vibrational spectroscopy, the fundamental band refers to a transition from the n = 0 state to n = 1, and the first overtone would be from the n = 0 state to n = 2. For carbon monoxide (CO), the fundamental occurs at 2143.4 cm-¹ and the first overtone at 4259.6 cm-¹. (a) For an anharmonic oscillator, the energy levels can be written (in wavenumbers) as 2 En ) ²³ = ve (n + ¹) - xeve (n +. + Find the values of ve and xeve from the fundamental and overtone transitions in CO. Report your results in units of cm-¹. (b) Use the values found for ve and xeve in part (a) to estimate the number of bound energy levels in CO. (Hint: For an anharmonic oscillator this number is determined by the point at which the spacing between consecutive levels goes to zero.) (c) If CO could be modeled as a Morse oscillator, and the values of ve and xeve provide energy levels consistent with the Morse potential what would be the value of the parameter D in units of cm-¹? How does this compare with the observed…arrow_forward
- In this question, we will consider the vibration of the diatomic molecule, H2, found in an eigenstate whose wave function is 1/4 1 p(x) V48 \T where a = ku/ħ. k is the force constant and u is the reduced mass. The vibrational frequency of H2 is 4401 cm-'. а) How many nodes are present in p(x)? b) What is the quantum number that characterizes p(x)? c) Calculate the vibrational energy of the H2 molecule when it is described by the eigenfunction p(x).arrow_forwardThe effective spring constant describing the potential energy of the HI molecule is 320 N/m and that for the HF molecule is 970 N/m. Calculate the minimum amplitude of vibration for (a) the HI molecule and (b) the HF molecule.arrow_forwarda) Starting from a general fornula of desity of States. g(k) dk= Vkdk 272 Show that g(w) dw= 3x Vw°dw for Phonons under the assumption thait the phonoh dre aicoustic, meaning U = does not depend 3. on W or k. 3N b) In a solid of N atoms, there are vibrational modes(phonons) with the highat frequercy Wp.arrow_forward
- The vibrational wavenumber of HBr is 264 cm-1 Evaluate the vibrational partition function of HBr at 298 K using both the exact and the approximate expressions.arrow_forwardThe valence election of chlorine is excited to a 3p state, (a) What is the magnitude of the election's orbital angular momentum? (b) What are possible values for the z-component of angular’ measurement?arrow_forward3. Atomic vibrations in a metal. Consider point ions of mass M and charge e immersed in a uniform sea of conduction electrons. The ions are imagined to be in stable equilibrium when at regular lattice points. If one ion is displaced a small distance r from its equilibrium position, the restoring force is largely due to the electric charge within the sphere of radius r centered at the equilibrium position. Take the number density of ions (or of conduction electrons ) as 3/(47R³), which defines R. (a) Show that the frequency of a single ion set into oscillation is @= (e²/MR³) ¹/2. (b) Estimate the value of this frequency for sodium, roughly. (c) From (a), (b), and some common sense, estimate the order of magnitude of the velocity of sound in metal.arrow_forward
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