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. (a) Calculate the minimum amplitude of vibration for the HBr molecule. (b) Calculate the minimum amplitude of vibration for the NO molecule.

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. (a) Calculate the minimum amplitude of vibration for the HBr molecule. (b) Calculate the minimum amplitude of vibration for the NO molecule.

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter11: Molecular Structure

Section: Chapter Questions

Problem 8P: The v = 0 to v = 1 vibrational transition of the HI molecule occurs at a frequency of 6.69 × 1013...

See similar textbooks

Related questions

Q: 1. The potential energy of a system of two atoms is given by the A relation ( E = В ) a stable…

Q: The CO molecule makes a transition from the J = 1 to the J = 2 rotational state when it absorbs a…

A: Let f be the incident photon’s frequency. The expression of the rotational kinetic energy of the…

Q: A hydrogen atom of mass 1.67 x 10 27 kg is attached to a very large'protein by a bond that behaves…

Q: I have 10 molecules. The collection has a total energy of 5au. The energy levels that the molecules…

A: Given data:total number of molecules = 10 molecules. The collection of total energy = 5au. The…

Q: (i) The potential energy of a diatomic molecule in terms of interatomic given by cance U(R) = R R…

A: Given: U(R)=-ARm+BRnhere A,B,m and n re constants

Q: The density of the distribution of the speed of motion of a molecule along the positive X axis has…

A: Given data: Density of the distribution, ρs=4a3πs2e-as2 Here, a=m2kT

Q: (a) What is the minimum donor doping required to convert silicon into a conductor based on the…

A: Known quantities: charge of an electron = e resistivity (rho) <10-3 ohm .cm Now, the…

Q: When are the rotational degrees of freedom of a diatomic molecule expected to contribute R to the…

A: This is a concept of heat capacity or specific heat.

Q: Atoms vibrate relative to one another in molecules with the bond acting as a spring. Consider the H…

A: Given: The force constant (Kf) for the H-Cl bond is 516.3 N.m-1. The mass of the hydrogen atom (mH)…

Q: Temperature is a measure of the molecule’s average of which of the following? (a) kinetic energy (b)…

A: The molecules of the hot gas move faster than the molecules of the cold gas.

Q: The Debye temperature of copper is 340 K. Calculate the highest possible vibrational frequency and…

A: Given: The temperature is T=10 k Boltzmann constant is K=1.38×10-23 J·k-1 The gas constant is R=8.31…

Q: Calculate the maximum permissible frequency of a crystal if you know that the mass of an atom is…

Q: At what temperature will the rms speed of a molecule is quarter of that of it has at a temperature…

Q: Show that the moment of inertia of a diatomic molecule composed of atoms of masses mA and mB and…

A: To calculate the moment of inertia of the the diatomic molecule.

Q: The rms (root-mean-square) speed of a diatomic hydrogen molecule at 50° C is 2000 m/s. Note that 1.0…

Q: Show that the moment of inertia of a diatomic molecule composed of atoms of masses mA and mB and…

A: Let rA and rB be the distance between the mass mA and mB from the center of mass of the diatomic…

Q: The Maxwell wheel has potential energy when suspended at a certain height, which it turns when…

A: Maxwell's wheel is the classic way of showing the interplay between potential energy and kinetic…

Q: potential energy (J) 5.0E-19 0 -5.0E-19 -1.0E-18 0.1 0.2 interactomic separation (nm) 0.3

Q: To give a helium atom nonzero angular momentum requires about 21.2 eV of energy (that is, 21.2 eV is…

A: The energy is given to helium, The Boltzmann constant,

Q: Q 2: Prove that in the hexagonal structure the vectors of the inverted lattice are given. According…

A: α*=α=90° β*=β=90° γ*=180-γ Draw the figure as below.

Q: The air is a gas mixture of oxygen, carbon dioxide, and Nitrogen. If the air can be treated as ideal…

A: Temperature = 100oC composition of air = oxygen , carbon dioxide and nitrogen Type of molecule =…

Q: Using the expression for the internal energy of a gas, as well as the definition of molar heat…

A: Ques:Using the expression for the internal energy of a gas, as well as the definition of molar heat…

Q: Calculate the RMS velocity of hydrogen molecule at 127 deg C. The density of hydrogen at NTP is 0.09…

A: Given: Temperature, T= 127o C = 400K Density of hydrogen gas = 0.09 kg/m3 To find: RMS velocity of…

Q: To determine the equilibrium separation of the atoms in the HCl molecule, you measure the rotational…

A: Given,The wavelength consisting with the rotational spectrum of HCl,60.4 mm, 69.0 mm, 80.4 mm, 96.4…

Q: One description of the potential energy of a diatomic molecule is given by the Lennard–Jones…

Q: The force constant of the Cl2 molecule is 323 Nm-1. Calculate the energy at the zero point of…

A: The fundamental vibrational frequency of a molecule is given by:v=12πkμwherev is fundamental…

Q: The air is a gas mixture of oxygen, carbon dioxide, and Nitrogen. If the air can be treated as ideal…

A: Composition of air = oxygen , carbon dioxide and nitrogen Temperature = 100o C To find = Average…

Q: What is the average energy of vibration of the molecules in a solid if the temperature is T = hf…

A: The solid has three degrees of freedom. According to equipartition theorem, each degree of freedom…

Q: To what temperature must a gas sample initially at 27°C be raised in order for the average energy of…

A: The initial absolute temperature of the gas is, T=27+273.15 K=300.15 K The average energy of a gas…

Q: A molecule has states with the following energies: 0, 1ε, 2ε, where ε = 1.0 x 10-20 J. Calculate…

Q: Let's consider the three atoms composing the molecule now have different masses and coordinate,…

A: Given M1= 142.54 kg M2= 82.55 kg M3= 8 kg D1= (3,6) D2= (1,6) D3= (5,9)

Q: The effective spring constant describing the potential energy of the HI molecule is 320 N/m and that…

A: (a) Determine the reduced mass of the HI molecule as follows.

Q: • Problem 3.22 The potential energy between the atoms of an hydrogen molecule can be modelled by…

A: To determine: The lowest angular frequency of the rotational motion and the frequency of the small…

Q: The frequency of vibration of the H2 molecule is 1.32*1014 Hz. (a) find the relative populations of…

Q: 5. Find the number of vibrational degrees of freedom of a COz molecule, if the average kinetic…

Q: Let f (e) be the Fermi Dirac distribution function and U be the chemical potential. Obtain the…

Q: The vibrational frequency n for Br2 is 323 cm-1 and the energy difference between its two lowest…

A: The relative population is the difference in energy from the ground state and the temperature of…

Q: In the motion of a diatomic molecule, the molecule oscillates as if there's a spring connecting the…

Q: Estimate the mean free path of a nitrogen molecule in a cylinder nitrogen at 2 atm and a temperature…

A: Given: The pressure of the gas is 2 atm. The temperature of the gas is 17oC. The radius is 1x10-10…

Q: Check both images please if possible.

Q: 5th exited

Q: A Sal has the deg denity posl.65g/cm ,w. 10% and Go=2.7. Using phase du. a. (bid ratio (e) b. hotal,…

Q: Although an ordinary H2 molecule consists of two identical atoms, this is not the case for the…

A: Given: The energy is E=0.0057 eV. The expression for temperature at which the heat capacity will…

Q: The primitive translation vectors of the hexagonal space lattice maybe taken as 32a --( 2 ) + (7) a1…

A: The primitive translation vectors at hexagonal space lattice may be taken as a1 =(31/2 a/2)x⏞+a/2 y⏞…

Q: The wavelength of the emitted photon from the hydrogen molecule H2 is 2.30 μm (micrometers) when the…

Q: What is the mean free path of a molecule? Express your answer with the appropriate units.

A: Given: Pressure P = 1×10-10 mm Hg Assume temperature T = 20o C = 293K

Concept explainers

Maxwell speed distribution

Maxwell-Boltzmann distribution or commonly known as Maxwell speed distribution, explains the division of the energy levels of the molecules of an ideal gas on the basis of the statistical theory. In 1859, Scottish physicist James Clerk Maxwell established the context for the distribution of molecular velocities for random molecules moving in a closed environment. This theory was generalized in 1871 by German physicist Ludwig Boltzmann. He improvised the theory to express the distribution of energy levels among different molecules.

Question

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.

(a) Calculate the minimum amplitude of vibration for the HBr molecule.

(b) Calculate the minimum amplitude of vibration for the NO molecule.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

The 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.
Consider the HCl molecule, which consists of a hydrogen atom of mass 1 u bound to a chlorine atom of mass 35 u. The equilibrium separation between the atoms is 0.128 nm, and it requires 0.15 eV of work to increase or decrease this separation by 0.01 nm. (a) Calculate the four lowest rotational energies (in eV) that are possible, assuming the molecule rotates rigidly. (b) Find the molecules spring constant and its classical frequency of vibration. (Hint: Recall that U=12Kx2.) (c) Find the two lowest vibrational energies and the classical amplitude of oscillation corresponding to each of these energies. (d) Determine the longest wavelength radiation that the molecule can emit in a pure rotational transition and in a pure vibrational transition.
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.
The 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?
N 2 has a molecular weight of 28.02 g/mol a bit larger than that of a Ne atom, 20.18 g/mol. (a) At a particular temperature, Z trans= 1.90 x 10 26 for Ne in a specific container. What is the translational partition function for a N2 molecule in this container at the same temperature? (b) At 100 K, the rotational partition function for N2is found to be 17.39. What would you expect it to be at 500 K?
One 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. Find, in terms of A and B, (a) the value r0 at which the energy is a minimum and (b) the energy E required to break up a diatomic molecule.
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?
The air is a gas mixture of oxygen, carbon dioxide, and Nitrogen. If the air can be treated as ideal gas at temperature 100 °C, what is the average kinetic energy for each of the molecule in air?(Consider Oxygen, Nitrogen, and carbon dioxide as diatomic molecule structure which consist of translational and rotational degree of freedom only. No vibration motion is considered) Boltzmann constant is kB = 1. 38 x 10 23 J/K
A rigid tank of volume V = 0.02 m3 contains carbon monoxide at a temperature of T0 = 25° C and a pressure of P0 = 9.00 × 105 Pa. This molecule should be treated as a diatomic ideal gas with active vibrational modes. a)The temperature of the gas increases by 10° C. Calculate the pressure of the gas in pascal at this increased temperature. b)Calculate the change to the internal energy of the gas in joules. c)Calculate the change in the entropy of the gas in joules per kelvin.
I'm hoping for a good explanation of how to do this. I'm also wondering why it matters if the configuration is linear or nonlinear? A triatomic molecule can have a linear configuration, as does CO2 (Figure a), or it can be nonlinear, like H2O (Figure b). Suppose the temperature of a gas of triatomic molecules is sufficiently low that vibrational motion is negligible. (a) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are linear?Eint/nT = ? (b) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are nonlinear?Eint/nT = ? At high temperatures, a triatomic molecule has two modes of vibration, and each contributes 0.5R to the molar specific heat for its kinetic energy and another 0.5R for its potential energy. (c) Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of the linear molecules. (Use…
please help quickly A molecule in a gas undergoes about 1.0 × 109 collisions in each second. Suppose that (a) every collision is effective in deactivating the molecule rotationally and (b) that one collision in 10 is effective. Calculate the width (in cm-1) of rotational transitions in the molecule.
A molecule in a gas undergoes about 1.0 × 109 collisions in each second. Suppose that (a) every collision is effective in deactivating the molecule rotationally and (b) that one collision in 10 is effective. Calculate the width (in cm-1) of rotational transitions in the molecule.