An electron (mass m) is contained in a rectangular corral of widths Lx= L and Ly =2L. (a) How many different frequencies of light could the electron emit or absorb if it makes a transition between a pair of the lowest five energy levels? What multiple of h/8mL2 gives the (b) lowest, (c) second lowest, (d) third lowest, (e) highest, (f) second highest, and (g) third highest frequency?

An electron (mass m) is contained in a rectangular corral of widths Lx= L and Ly =2L. (a) How many different frequencies of light could the electron emit or absorb if it makes a transition between a pair of the lowest five energy levels? What multiple of h/8mL2 gives the (b) lowest, (c) second lowest, (d) third lowest, (e) highest, (f) second highest, and (g) third highest frequency?

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

Chapter5: Matter Waves

Section: Chapter Questions

Problem 13P

See similar textbooks

Similar questions

Using the average speed of a gas, (8RT/piMW)^1/2 determine the average de Broglie wavelength for an He atom at 25 °C and at 500 °C.How fast would the He atom need to travel in order to have the same linear momentum as a 500 nm photon?
The light observed that is emitted by a hydrogen atom is explained by a simple model of its structure with one proton in its nucleus and an electron bound to it, but only with internal energies of the atom satisfying EH=−RH/n2EH=−RH/n2 where RHRH is the Rydberg constant and nn is an integer such as 1, 2, 3 ... and so on. When a hydrogen atom in an excited state emits light, the photon carries away energy and the atom goes into a lower energy state. Be careful about units. The Rydberg constant in eV is 13.605693009 eV That would be multiplied by the charge on the electron 1.602× 10-19 C to give 2.18× 10-18 J A photon with this energy would have a frequency f such that E=hf. Its wavelength would be λ = c/f = hc/E. Sometimes it is handy to measure the Rydberg constant in units of 1/length for this reason. You may see it given as 109737 cm-1 if you search the web, so be aware that's not joules. The following questions are intended to help you understand the connection between…
When a hydrogen atom is in its ground state, what are the shortest and longest wavelengths of the photons it can absorb without being ionized?
If the work function of a metal is 3.2 eV, what is the maximum wavelength that a photon can have to eject a photoelectron from this metal surface?
The binding energies of K-shell and L-shell electrons in copper are 8.979 and 0.951 keV, respectively. If a Ka x ray from copper is incident on a sodium chloride crystal and gives a first-order Bragg reflection at an angle of 74.1° measured relative to parallel planes of sodium atoms, what is the spacing between these parallel planes?
If a photon of wavelength 0.0665 nm hits a free electron and is scattered at an angle of 35◦ from its original direction, findat. the change in wavelength of this photon,b. the wavelength of the scattered photon,vs. the change in energy of the photon (is it a loss or a gain?), and d. the energy gained by the electron.
An atom (not a hydrogen atom) absorbs a photon whose associated wavelength is 375 nm and then immediately emits a photon whose associated wavelength is 580 nm. How much net energy is absorbed by the atom in this process?
When light of wavelength 350 nm falls on a potassium surface, electrons having a maximum kinetic energy of 1.31 eV are emitted. Find (a) the work function of potassium, (b) the cutoff wavelength, and (c) the frequency corresponding to the cutoff wavelength
What is the minimum frequency in (THz) of light needed to eject electrons off a metal with a work function of 10.00 eV?
A collection of atoms has 20% of the sample in a state 7.60 eV above the ground state. If these emit coherent radiation, what is the wavelength of the laser light produced in nanometers? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) Give your answer as a whole number.
For the thermal radiation from an ideal blackbody radiator with a surface temperature of 2000 K, let Ic represent the intensity per unit wavelength according to the classical expression for the spectral radiancy and IP represent the corresponding intensity per unit wavelength according to the Planck expression.What is the ratio Ic/IP for a wavelength of (a) 400 nm (at the blue end of the visible spectrum) and (b) 200 mm (in the far infrared)? (c) Does the classical expression agree with the Planck expression in the shorter wavelength range or the longer wavelength range?
Through what angle must a 200 keV photon be scattered by a free electron so that the photon loses 10% of its energy?