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A hydrogen atom bonded to a surface is acting as a harmonic oscillator with a classical...
Hydrogen molecule bonded to a surface is acting as a quantized harmonic oscillator with a force...
Hydrogen molecule bonded to a surface is acting as a quantized harmonic oscillator with a force constant of 300 Nm^-1. a) What is the second to the lowest possible vibrational energy of this system? b) What is the wavefunction of the photon whose energy matches the difference between these two energy levels?
2. (10 pts) Hydrogen molecule bonded to a surface is acting as a quantized harmonic oscillator...
2. (10 pts) Hydrogen molecule bonded to a surface is acting as a quantized harmonic oscillator with a force constant of 300 Nm! What is the wavefunction of the photon whose energy matches the difference between these two energy levels? (10 pts=5 points for correct work shown, 2 points for the correct units, and 3 points for correct answer)
Find the frequency of revolution of the electron in the classical model of the hydrogen atom....
Find the frequency of revolution of the electron in the classical model of the hydrogen atom. In what region of the spectrum are electromagnetic waves of this frequency?
a) For the hydrogen atom, find the change in energy, AE in a transition of hydrogen...
a) For the hydrogen atom, find the change in energy, AE in a transition of hydrogen between the n=7 and n=1 energy levels. b) What is the wavelength of light that corresponds to this energy? c) Is it within the visible, infrared or ultra-violet region of the electromagnetic spectrum?
3. The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an...
3. The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Consider an electron trapped by a one-dimensional harmonic potential V(x)=-5 mo?x” (where m is the electron mass, o is a constant angular frequency). In this case, the Schrödinger equation takes the following form, **...
Question no 6.1, statistical physics by Reif Volume 5 Problems 6.1 Phase space of a classical harmonic oscillator The en...
Question no 6.1,
statistical physics by Reif Volume 5
Problems 6.1 Phase space of a classical harmonic oscillator The energy of a one-dimensional harmonic oscillator, whose position coordinate is x and whose momentum is p, is given by where the first term on the right is its kinetic and the second term its potential energy. Here m denotes the mass of the osellating particle and a the spring constant of the restoring force acting on the particle. Consider an ensemble...
(10 pts) The two calculations below pertain to the quantum harmonic oscillator (qho). Relevant expressions for...
(10 pts) The two calculations below pertain to the quantum harmonic oscillator (qho). Relevant expressions for the qho states and energies needed are given by: En-(n +-)ћ1_ and n-AnHn(ye- Two 1g masses are attached by a spring with a force constant k-500 kg/s2. Calculate the zero point energy of this system. How fast would this system have to move to have that much translational energy? a. b. Calculate the wavenumber and wavelength of radiation absorbed when a quantum harmonic oscillator...
One can assume a quantum mechanical harmonic oscillator model for the N-H stretching vibrations of the...
One can assume a quantum mechanical harmonic oscillator model for the N-H stretching vibrations of the peptide bonds. For the harmonic oscillator the energy levels are given by: E, = (V+})ħw where: W= /k/ u In the above express k is the force constant and u is the reduced mass. (a) Write the Schrödinger equation in terms of the reduced mass u, being sure to define all symbols. (b) Calculate the frequency of the infrared radiation absorbed by the N-H...
1. How many lines would be in the emission spectrum of hydrogen if the hydrogen atom...
1. How many lines would be in the emission spectrum of hydrogen if the hydrogen atom had only 4 energy levels? 2. What was the initial energy level of an electron if it was excited by a photon of wavelength 0.656µm and jumped to an energy level of 3? 3 .Calculate the frequency of visible light emitted by electron drop from n=233000 in Balmer series of hydrogen atom.
What is the highest energy photon that can be absorbed by a ground state hydrogen atom...
What is the highest energy photon that can be absorbed by a ground state hydrogen atom Without causing ionization? What is the wavelength of this radiation? What part of the electromagnetic spectrum does this photon belong?
2. (10 pts) Hydrogen molecule bonded to a surface is acting as a quantized harmonic oscillator with a force constant of 300 Nm! What is the wavefunction of the photon whose energy matches the difference between these two energy levels? (10 pts=5 points for correct work shown, 2 points for the correct units, and 3 points for correct answer)
Find the frequency of revolution of the electron in the classical model of the hydrogen atom. In what region of the spectrum are electromagnetic waves of this frequency?
a) For the hydrogen atom, find the change in energy, AE in a transition of hydrogen between the n=7 and n=1 energy levels. b) What is the wavelength of light that corresponds to this energy? c) Is it within the visible, infrared or ultra-violet region of the electromagnetic spectrum?
3. The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Consider an electron trapped by a one-dimensional harmonic potential V(x)=-5 mo?x” (where m is the electron mass, o is a constant angular frequency). In this case, the Schrödinger equation takes the following form, **...
Question no 6.1,
statistical physics by Reif Volume 5
Problems 6.1 Phase space of a classical harmonic oscillator The energy of a one-dimensional harmonic oscillator, whose position coordinate is x and whose momentum is p, is given by where the first term on the right is its kinetic and the second term its potential energy. Here m denotes the mass of the osellating particle and a the spring constant of the restoring force acting on the particle. Consider an ensemble...
(10 pts) The two calculations below pertain to the quantum harmonic oscillator (qho). Relevant expressions for the qho states and energies needed are given by: En-(n +-)ћ1_ and n-AnHn(ye- Two 1g masses are attached by a spring with a force constant k-500 kg/s2. Calculate the zero point energy of this system. How fast would this system have to move to have that much translational energy? a. b. Calculate the wavenumber and wavelength of radiation absorbed when a quantum harmonic oscillator...
One can assume a quantum mechanical harmonic oscillator model for the N-H stretching vibrations of the peptide bonds. For the harmonic oscillator the energy levels are given by: E, = (V+})ħw where: W= /k/ u In the above express k is the force constant and u is the reduced mass. (a) Write the Schrödinger equation in terms of the reduced mass u, being sure to define all symbols. (b) Calculate the frequency of the infrared radiation absorbed by the N-H...
What is the highest energy photon that can be absorbed by a ground state hydrogen atom Without causing ionization? What is the wavelength of this radiation? What part of the electromagnetic spectrum does this photon belong?
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