Concept explainers
Verify that the following wavefunctions are indeed eigenfunctions of the Schrödinger equation, and determine their energy eigenvalues.
(a)
(b)
(c)
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Physical Chemistry
- An electron is confined to a square well of length L. What would be the length of the box such that the zero-point energy of the electron is equal to its rest mass energy, mec2? Express your answer in terms of the parameter λC = h/mec, the ‘Compton wavelength’ of the electron.arrow_forward(a) What are the possible values for mℓ when the principal quantum number (n) is 2 and the angular momentum quantum number (ℓ) is 0? (b) What are the possible values for mℓ when the principal quantum number (n) is 3 and the angular momentum quantum number (ℓ) is 2?arrow_forwardWhat values of J may occur in the terms (i) 3D, (ii) 4D, (iii) 2G? How many states (distinguished by the quantum number MJ) belong to each level?arrow_forward
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- The speed of a certain electron is 995 km s−1. If the uncertainty in its momentum is to be reduced to 0.0010 per cent, what uncertainty in its location must be tolerated?arrow_forwarda. Normalize the wavefunction Ψ(x) = 1 in a space of 0 ≤ x ≤ ℓ b. Find the probability of finding the particle in the subspace [0,ℓ/2 ] c. Find the most-likely position of the particle in entire space d. Find the most-likely position of the particle in the subspace [0,ℓ/3 ]arrow_forwardConsider a fictitious one-dimensional system with one electron.The wave function for the electron, drawn below, isψ (x)= sin x from x = 0 to x = 2π. (a) Sketch the probabilitydensity, ψ2(x), from x = 0 to x = 2π. (b) At what value orvalues of x will there be the greatest probability of finding theelectron? (c) What is the probability that the electron willbe found at x = π? What is such a point in a wave functioncalled?arrow_forward
- Sketch the orientation of the allowed values of l=1 for the shell n=2arrow_forwardquantum chemistry Evaluate the probability density at r=1.2a0 for an electron in a 2s orbital of a hydrogen atomarrow_forwardConsider a particle trapped in a 1D box with zero potential energy with walls at x = 0 and x = L. The general wavefunction solutions for this problem with quantum number, n, are: ψn(x) = sqrt(2/L sin(npix/L)) The corresponding energy (level) for each wavefunction solution is: En = (n^2h^2)/(8mL^2) Is the particle always uniformly distributed throughout the box? Explain your answer.arrow_forward
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