
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 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 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)
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?
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?
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...
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?
The hydrogen atom can absorb light of wavelength 1094nm. (a) In what region of the electromagnetic spectrum is this absorption found? (b) Determine the initial and final values of n associated with this absorption.
(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...
When an electron of an excited hydrogen atom descends, from an initial energy level (ni) to a lower (nf), characteristic electromagnetic radiation is emitted. The Bohr model of the H-atom allows the calculation of ?E for any pair of energy levels. ?E is related to the wavelength (?) of the radiation according to Einstein's equation ( ?E = [(hc)/?]). Distinct series of spectral lines have been classified according to nf: Lyman series:nf=1 (91<?<123 nm; near-UV). Balmer series:nf=2 (365<?<658 nm; visible)....