The figures below show the wave function describing two different states of a particle inan infinite square well. The number of nodes (within the well, but excluding the walls) ineach wave function is related to the quantum number associated with the state itrepresents:Wave function Anumber of nodes = n-1Wave function BMDetermine the wavelength of the light absorbed by the particle in being excited from thestate described by the wave function labelled A to the state described by the wavefunction labelled B. The distance between the two walls is 1.00 × 10-10 m and the mass ofthe particle is 1.82 × 10-30 kg. Enter the value of the wavelength in the empty box below.Your answer should be specified to an appropriate number of significant figures.wavelength=nm.

Step 1: Step 2: Step 3: Step 4:

Answered: The figures below show the wave…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Similar questions

Particle of mass m moves in a three-dimensional box with edge lengths L1, L2, and L3. (a) Find the energies of the six lowest states if L1 =L, L2 = 2L, and L3 = 2L. (b) Which if these energies are degenerate?
The wave function for a quantum particle is given by ?(?)=??between ?=0and ?=1.00, and ?(?)=0elsewhere. Find (a) the value of the normalization constant ?, (b) the probability that the particle will be found between ?=0.300and ?=0.400, and (c) the expectation value of the particle’s position.
For 3-D system, the Schrödinger equation changes. a) True b) False
Which is not considered a wave function in the range in which it is defined?
An electron moving in a box of length ‘a’. If Z1 is the wave function at x1 = a/4 with n=1 and Z2 at x = a/4 for n=2 find Z1/Z2
Chapter 39, Problem 009 Suppose that an electron trapped in a one-dimensional infinite well of width 144 pm is excited from its first excited state to the state with n 9. (a) What energy must be transferred to the electron for this quantum jump? The electron then de- excites back to its ground state by emitting light. In the various possible ways it can do this, what are the (b) shortest, (c) second shortest, (d) longest, and (e) second longest wavelengths that can be emitted? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
Which of the following is/are correct for the equation y(x) dx defined for a particle whose state function is y(x) (11) (iii) This equation gives the probability of the particle with the range x to X₂. This equation applies to the particle moving in any dimension. This equation defines relation between the state function and the probability with the range x; to x₂- (a) Only (1) (b) (ii) and (iii) (c) (i) and (iii) (d) (i) and (ii)
An electron is trapped in a one-dimensional infinite potential well. For what (a) higher quantum number and (b) lower quantum number is the corresponding energy difference equal to the energy of the n9 level? (c) Can a pair of adjacent levels have an energy difference equal to the energy of the n4?
4) Consider the one-dimensional wave function given below. (a) Draw a graph of the wave function for the region defined. (b) Determine the value of the normalization constant. (c) What is the probability of finding the particle between x = o and x = a? (d) Show that the wave function is a solution of the non-relativistic wave equation (Schrodinger equation) for a constant potential. (e) What is the energy of the wave function? (x) = A exp(-x/a) for x > o (x) = A exp(+x/a) for x < o
Calculate the probability and probability density to find the particle between X = 0 and X = a /n when it is in the n state
A particle is in a three-dimensional cubical box that has side length L. For the state nX = 3, nY = 2, and nZ = 1, for what planes (in addition to the walls of the box) is the probability distribution function zero?
Problem 3. Consider the two example systems from quantum mechanics. First, for a particle in a box of length 1 we have the equation h² d²v 2m dx² EV, with boundary conditions (0) = 0 and (1) = 0. Second, the Quantum Harmonic Oscillator (QHO) V = EV h² d² 2m da² +ka²) 1 +kx² 2 (a) Write down the states for both systems. What are their similarities and differences? (b) Write down the energy eigenvalues for both systems. What are their similarities and differences? (c) Plot the first three states of the QHO along with the potential for the system. (d) Explain why you can observe a particle outside of the "classically allowed region". Hint: you can use any state and compute an integral to determine a probability of a particle being in a given region.

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