An electron confined to a one-dimensional box oflength 0.70 nm jumps from the n = 2 level to theground state.Part AWhat is the wavelength (in nm) of the emitted photon?Express your answer to two significant figures and include the appropriate units.ΜΑ?A =ValueUnitsSubmitRequest AnswerProvide Feedback

Given length of one-dimensional box (L) = 0.7 nm = 0.7 * 10-9 m,To find the wavelength of the photon…

Answered: An electron confined to a…

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 11P

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Suppose an electron is confined to a region of length 0.1 nm (of the order of the size of a hydrogen atom) and its kinetic energy is equal to the ground state energy of the hydrogen atom in Bohr's model (13.6 eV). (a) What is the minimum uncertainty of its momentum? What fraction of its momentum is it? (b) What would the uncertainty in kinetic energy of this electron be if its momentum were equal to your answer in part (a)? What fraction of its kinetic energy is it?
a) The element helium is named for the Sun because that is where it was first observed. What is the shortest wavelength that one would expect to observe from a singly ionized helium atom in the atmosphere of the Sun? b) Suppose light with a wavelength of 388.9 nm is observed from singly ionized helium. What are the initial and final values of the quantum number nn corresponding to this wavelength? Enter your answers numerically separated by a comma
a. Conceptually, discuss the particle-wave duality of light. Discuss the implications of this in combination with the de Broglie (pronounced “de Broy”) equation. b. The electron of a hydrogen atom is usually no further than 1.0 Å from the proton. We can therefore say the upper limit of the radius of an isolated hydrogen atom is roughly 1.0 Å. How does the de Broglie wavelength of the electron compare to this radius? (The velocity of an electron in the first principal energy level is about 2.2 x 106 m/s). Explain why wave-particle duality is so important for quantum mechanics, yet not required in macroscopic systems that are well described by classical mechanics. c. Comment as to whether neutrons with velocity 4.14 x 103 m/s may be used to determine structures of molecules in a diffraction-based experiment. You may consider the relevant distance between atoms in molecules to be on the order of 1 Å.
Monochromatic light from a laser shines onto a gold surface and produces photoelectrons with maximum kinetic energy KEmax = 3 eV. What is the wavelength of the laser light? Assume a work function of 5.10 eV for gold.Please give your answer in units of nm, rounded to 1 decimal place. I.e, the answer you should enter should have the form: XX.X nm.
The electron interference pattern as shown was made by shooting electrons with 50 keV of kinetic energy through two slits spaced 1.0 mm apart. The fringes were recorded on a detector 1.0 m behind the slits.a. What was the speed of the electrons? (The speed is large enough to justify using relativity, but for simplicity do this as a nonrelativistic calculation.)b. Figure is greatly magnified. What was the actual spacing on the detector between adjacent bright fringes?
The work function of aluminum is 4.26 ev. What is the maximum velocity of an electron emitted from aluminum after the absorption of a photon of wavelength 117 nm. Give your answer in m/s. Round your answer to 2 decimal places. Add your answer Question 10 A photon Compton scatters from an electron. At what scattering angle for the photon will the electron acquire the largest kinetic energy? 45 degrees 90 degrees C o degress D 180 degrees
Solve the following problem: Use rest mass energy of the electron 0.5 MeV Consider an atomic level with quantum numbers n = 2,l = 1 and maximum total angular momentum. a. Find the first order relativistic correction to this level, in electron- volts. b. Find the first order spin-orbit correction to this level, in electron-volts. C. Use your result in parts a and b to find the energy of that level.
A. If the position of a chlorine ion in a membrane is measured to an accuracy of 1.50 µm, what is its minimum uncertainty in velocity (in m/s), given its mass is 5.86 10-26 kg? B. If the ion has this velocity, what is its kinetic energy in eV? (Compare this with typical molecular binding energies of about 5 eV.)
A sodium atom in one of the states labeled “Lowest excited levels” in Fig. remains in that state, on average, for 1.6 * 10-8 s before it makes a transition to the ground state, emitting a photon with wavelength 589.0 nm and energy 2.105 eV. What is the uncertainty in energy of that excited state? What is the wavelength spread of the corresponding spectral line?
Q°: The line width of a helium-neon laser is 10° Hz. The operating wavelength is 632.8 mm and the power is 1mW. a. How many photons are emitted per second? b. If the output beam is Imm in diameter, at what temperature would a blackbody have to be in order to emit the same number of photon from an equal area and over the same frequency interval as the laser?
Problem 4: a. For Compton scattering, what photon scattering angle provides the maximum possible kinetic energy to the electron? (Please explain your answer. Hint: What angle 6 makes the wavelength difference as large as possible?) b. In this case where the electron gains the maximum kinetic energy, if the wavelength of the incident photon was 0.004960 nm, what kinetic energy did the electron gain?
An X-ray photon moving along the x-direction is scattered by a stationary electron. The initial frequency of the photon is fi = 8 x 10t° Hz and the final frequency is fr = been scattered. In other words finesthe angle 0 that the outgoing photon makes with respect to the x-axis. Give your answer in degrees to 3 significant figures. Sketch a diagram showing the directions of the initial and final momenta. 7.75 x 1018 Hz. Find the direction of the photon's momentum after it has

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