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6.1: Where is the Electron?
ΔV=(Xao3)  ∴  ao3=ΔV/X
ψ(r,θ,φ)=(πao3)-1/2exp(-r/ao)
ψ2(r,θ,φ)=(πao3)-1exp(-2r/ao)
The probability in ΔV at r=0 is: X3π-1
The probability in ΔV at r=ao is: X3π-1e-2
The probability in ΔV at r=2ao is: X3π-1e-4


6.2: Orbital Angular Momentum
These answers are for n=4
a. There are 16 orbital states.
b. Emax = .8504 eV
c. Lz max = 3 h/(2π)
d. L2 = 12 (h/(2π))2


6.3: Hydrogen 2p Wave Function
a. The probability density is greatest along the 3 axis.
b. Probability density = 1/(32*pi)*(1/ao)^3*exp(-1)*ao^3 per ao3.
c. θ = 45 degrees.


6.4: Hydrogen Energy Levels
a. n = 3
b. answer = 4.2 eV


6.5: Superheavy Noble Gas
Z = 118


NOTE ABOUT HOMEWORK B:  THESE ANSWERS MAY NOT BE CORRECT.  USE THEM AT YOUR OWN RISK.
HomeworkB 06
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1. Solutions of the Schrodinger equation in a hydrogen atom are characterized by their principal number n, their orbital angular momentum number l and their magnetic (azimuthal) number m. There are certain rules about the range of these numbers. Which of the combinations of (n,l,m ) below does not satisfy these rules, and is thus impossible? The impossible state is described by: 
 (n,l,m ) = ( 3,1,2 )
2. Assume that this is the measured probability density (per unit volume) of an electron in a hydrogen atom.
Which of the following statements about the state of the electron has to be true? 
 The orbital angular momentum number l = 0 and the magnetic number m = 0.

Consider wave functions which are linear combinations of functions Yl,m(θ,φ) described in the lecture.
3. Suppose that the angular dependence of a wave function is ψ(θ, φ) = N(1 + cosθ). N is the normalization constant. If we measure l and m, what answers might we get? 
 (l,m) = (0,0) and (1,0)
4. Consider a bunch of electrons. Each has this wave function, a superposition of two different Yl,m: ψ = aYl1, m1 + bYl2, m2
Suppose you know (by making many (l,m) measurements) that the probability of obtaining (l 1, m1) is 1/4 and the probability of obtaining (l 2, m2) is 3/4. Which of these sets of (a,b) values will give you the observed probabilities? 
 (a,b) = (1/2, √3/2)
5. Consider a similar wave function, ψ = aYl1,m1 - bYl2,m2 . a and b remain the same but there is now a minus sign. How will the probabilities compare to the previous situation? 
 X This is an illegal wave function, because negative probabilities aren't allowed.