Construct the wavefunction V(r, 0, ø) for an H atoms' electron in the state 2p,. Please note that in order to have a real-valued wavefunction of p, orbital(see below), you need to do a linear superposition of the corresponding spherical harmonics for the angular part. Use the spherical harmonics table below. Show that the superposition you selected indeed results in a real orbital; however, you do not need to simplify the expressions further or normalize the wavefunction.

Construct the wavefunction V(r, 0, ø) for an H atoms' electron in the state 2p,. Please note that in order to have a real-valued wavefunction of p, orbital(see below), you need to do a linear superposition of the corresponding spherical harmonics for the angular part. Use the spherical harmonics table below. Show that the superposition you selected indeed results in a real orbital; however, you do not need to simplify the expressions further or normalize the wavefunction.

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter10: Introduction To Quantum Mechanics

Section: Chapter Questions

Problem 10.28E: A particle on a ring has a wavefunction =eim, where =0to2 and m is a constant. a Normalize the...

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Based on the trend shown in Figure 11.5, draw the probability distribution of a harmonic oscillator wavefunction that has a very high value of n. Explain how this is consistent with the correspondence principle.
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For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the probability that the particle exists in the following intervals? a x=0to0.02ab x=0.24ato0.26a c x=0.49ato0.51ad x=0.74ato0.76a e x=0.98ato1.00a Plot the probabilities versus x. What does your plot illustrate about the probability?
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Is the uncertainty principle consistent with our description of the wavefunctions of the 1D particle-in-a-box? Hint: Remember that position is not an eigenvalue operator for the particle-in-a-box wavefunctions.
What are the degeneracies of the H atom wavefunctions when spin is accounted for? Give a general formula.
If 1 and 2 are the individual wavefunctions for electron 1 and electron 2, identify each overall wavefunction as symmetric or antisymmetric with respect to exchange of the two electrons. i.e., 1 becomes 2 and vice versa. a=1+2 b=12 c=12+22 d=sin1+sin2 d=cos1cos2
A particle on a ring has a wavefunction =eim, where =0to2 and m is a constant. a Normalize the wavefunction, where d is d. How does the normalization constant depend on the constant m? b What is the probability that the particle is in the ring indicated by the angular range =0to2/3? Does this answer make sense? How does the probability depend on constant m?
Spin orbitals are products of spatial and spin wavefunctions, but correct antisymmetric forms of wavefunctions for multielectron atoms are sums and differences of spatial wavefunctions. Explain why acceptable antisymmetric wavefunctions are sums and differences that is, combinations instead of products of spatial wavefunctions.
In exercise 10.41a, the wavefunction is not normalized. Normalize the wavefunction and verify that it still satisfies the Schrdinger equation. The limits on x are 0 and 2. How does the expression for the energy eigenvalue differ?
What is the physical explanation of the difference between a particle having the 3-D rotational wavefunction 3,2 and an identical particle having the wavefunction 3,2?