More Quantum Mechanics II PREFLIGHT

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The following three questions refer to the material you were to read in preparation for the lesson. Questions one and three require you to write a three or four sentence response. Number two is a multiple choice question. Click in the appropriate circle.

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1. Hydrogenic Atom Wave Functions

(All questions are based on the quantum solution for the hydrogen atom. Please scroll to bottom of page. I couldn't nest html "FORM", so it had to go to the bottom.)

Before quantum mechanics got off the ground, the spectroscopists had named all the "families" of lines, of which the Lyman and Balmer series are the most famous. In addition, there were "splitting" of lines that could be seen with high resolution spectroscopes, and these families were given additional names. Thus, for quantum number (n,l=0,m=0) the spectroscopist called it "s" for "sharp"; (n>1,l=1,m) where "p", (n>2,l=2,m) were "d" for "diffuse", then came "f" for "fine" and finally they just gave up and used the alphabet, "g,h,..."
Describe in words what a "f" orbital state looks like, and give its quantum numbers. What does the last number, the "m" quantum number do to the "f" orbital?




2.

Which quantum number determines the average distance that the electron spends from the nucleus?

The first "principal" quantum number, "n".

The second "orbital" quantum number, "l".

The third "orbital magnetic" quantum number "m".

All quantum numbers have an effect on radius.


3.

A Dutch spectroscopist named Zeeman, noticed that if he put a hydrogen lamp (a tube of glowing hydrogen like a fluorescent lamp) in a magnetic field, and looked at the spectral lines coming out, some of the lines he was looking at suddenly split into triplets of lines, where the distance between the lines depended on the magnetic field. Spectroscopists can use this same effect to measure the magnetic field on the surface of distant stars, and in fact, MSFC pioneered a technique using this to measure the vector magnetic field of our Sun's surface. Since the energy of an electron depends only on its average distance from the nucleus, how can a magnetic field affect the position of an electron? What quantum number is involved?





honors extra

The lowest energy state of a hydrogen atom is the (n=1,l=0,m=0) state. But it still has a wiggly wave function which means, by Schroedinger's equation, it still has kinetic energy. If we can't get the electron to stop moving, then does that mean at absolute zero, the atom (and electron) is still bouncing around? Do atoms ever stop moving at absolute zero? Can we use this energy for anything?





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I received no help from anyone on this assignment.




1. Hydrogenic Atom Wave Functions

n=
l=
m=
Note: Right click on any applet to make a copy of the image.

This applet examines the properties of the wave functions for hydrogenic atoms.  The top graphs are the wave functions  generated by solutions of the polar and radial equations.  Halliday and Resnick give only the radial (right hand plot) equations. They ignore the effect of angular momentum, which has separate solutions (left hand plot). The full solution is happily just the product of the radial and angular solutions. The polar solutions used here are the unnormalized associated Legendre polynomials, Plm(q,f).  Note that the x and z coordinates range from -1 to +1.  The radial solutions used here are the associated Laguerre polynomials scaled with a0 = 1.  The graph in the lower left corner is a plot corresponding to the product of the upper two graphs. 

The Physlets contained in this exercise package were written by Cabell Fisher, Jim Nolen, and Wolfgang Christian .  This lab was prepared by Dan Boye.