What is the value of quantum number, n, for a 1-dimensional particle-in-a-box system in which the normalized wave function is 4' = sin (4). The box boundaries are at x=0 and x=3n. The potential energy is zero when 0 < x < 3n and o outside of these boundaries.
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- A proton is confined in box whose width is d = 750 nm. It is in the n=3 energy state. What is the probability that the proton will be found within a distance of d/n from one of the walls? [Hint: the average value sin^2x over one or more of its cycles is 1/2] PLEASE PLEASE include a sketch of U(x) and Ψ(x)The nucleus of a typical atom is 5.0 fm (1 fm = 10-15 m) in diameter. A very simple model of the nucleus is a onedimensional box in which protons are confined. Estimate the energy of a proton in the nucleus by finding the first three allowed energies of a proton in a 5.0-fm-long box.(a) Find the normalization constant A for a wave function made up of the two lowest states of a quantum particle in a box extending from x= 0 to x = L: x) = A sin + 4 sin L. (b) A particle is described in the space -aSxs a by the wave function (x) = A cos + B sin 2a a Determine the relationship between the values of A and B required for normalization.
- QUESTION 7 Use the Schrödinger equation to calculate the energy of a 1-dimensional particle-in-a-box system in which the normalized wave function is 4' = e sin(6x). The box boundaries are at x=0 and x=r/3. The potential energy is zero when 0 < x <- and o outside of these boundaries. 18h? m h2 8m h2 36n2m none are correctA 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?A particle is in the n = 9 excited state of a quantum simple harmonic oscillator well. A photon with a frequency of 3.95 x 1015 Hz is emitted as the particle moves to the n = 7 excited state. What is the minimum photon frequency required for this particle to make a quantum jump from the ground state of this well to the n = 8 excited state? (Give your answer in Hz.)
- In the lab you make a simple harmonic oscillator with a 0.15-kg mass attached to a 12-N/m spring. (a) If the oscillation amplitude is 0.10 m, what is the corresponding quantum number n for the quantum harmonic oscillator? (b) What would be the amplitude of the quantum ground state for this oscillator? (c) What is the energy of a photon emitted when this oscillator makes a transition between adjacent energy levels? Comment on each of your results.An electron is in an infinite potential well of width 364 pm, and is in the normalised superposition state Ψ=cos(θ) ψ5-sin(θ) i ψ8. If the value of θ is -1.03 radians, what is the expectation value of energy, in eV, of the electron?