PHYS343 Spring 2007
Homework #5
Due Friday March 30,2007 COB
1.
For the ground state of hydrogen, calculate the probability of finding the electron
in the interval a o  r  4 a o .
2.
(a) For the ground state of the hydrogen atom, determine the radial distance for
which the probability of finding the electron less than this distance is 90%. Give a
numerical answer to two significant figures. (b) Repeat the calculation for a 99%
probability.
3.
Estimate the probability that the electron will be found inside the proton for (a)
the 2s state and (b) the 2p state. Assume that a proton has a radius of
approximately 1 fm.
4.
(a) What are the possible values of L and Lz for the 3p state? (b) For the 3d state?
5.
A hydrogen atom is in an excited state, n=5. (a) What are the possible values of
the quantum numbers  and m  ? (b) What are the possible values of the orbital
angular momentum L?
6.
(a) Prove that the function ψ  C r e
 r2δ
cosθ  is a solution of the hydrogen
2
atom, where δ 
. (b) Determine the energy of the state. (c) What is the
mke 2
value of the angular momentum L?
7.
Prove that the operator for the x component of orbital angular momentum is given
by
 cosθ cos   

L x   i   sin   
.
θ
sin θ 
 

8.
Consider a model of an electron as a tiny uniform sphere of size 10-18 m
corresponding to the experimental limit on possible electron structure. Suppose
that the electron intrinsic angular momentum is due to the spinning motion of a
sphere with an angular frequency ω . Calculate the value of ω . Explain why this
is a “bad” model of electron spin.
9.
If you modeled the nucleus of hydrogen as a 1-D particle in a box with the
distance between the walls of approximately 1 fm, what would be the energies of
the first four states?
10.
Assuming an electron is trapped in a 2-D square box whose sides are 1
nanometer. What are the energy values of the four lowest states?