CH 301H Fall 2007 Exam III
18
CH 301H 54785 Fall 2007
November 20, 2007
Professor Campion
Exam III
1.
What is a wavefunction?
What observable properties of a system (particle in a box, atom etc.)
can we find if we know the wavefunction and how do we find them?
(Points: 5)
ANS:
Wave function is a function that describes the properties of a particle; its square is proportional
to the probability of finding the particle at a particular point in space.
Observable properties of a system are the amplitude, number of nodes, by setting the wave
function=0 and the derivative of wave function =0; probability of finding a particle in a certain
special point, by squaring and normalizing the wave function; energy and momentum, etc.
2.
Consider a particle in a onedimensional box.
(Points: 15)
a)
Sketch the wavefunction for the
n
= 2 state. Identify nodes if any (how many and
where are they?).
b)
Sketch the probability density distribution for the particle. What does that mean?
Where is the particle most likely to be found? Least likely to be found? Does it have to
jump to get from one place to another? If so, why, if not, why not?
c)
Carrots get their color from a pigment called carotene (I’m not making this up). The
particle in a box model can be used to calculate the color of the light absorbed by
carotene.
Let’s assume that the
π
electrons are free to move in one dimension in a “box”
whose length is1.8 nm and that there are 22
π
electrons. 2 electrons can fill each level
(why? Answer this.) so the lowest energy absorption occurs when an electron is excited
from the
n
=
11 state to the
n
= 12 state. Calculate the wavelength of the light absorbed.
What color is
it? Since the color of a carrot is given by the light that is reflected and not
absorbed, does your answer make sense?
d)
Why is
n
= 0 not allowed for a particle in a box?
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28
Answers sheet for Q2:
ANS:
a)
one node at L/2
b)
It means that the probability of finding the particle at a particular point in space.
It’s most likely to be found at L/4 and 3L/4, since
2
2
ψ
reaches its maximum; it’s least to be found
at L/2, since
2
2
=0.
The particle doesn’t need to jump at here, since we consider it as a wave, it can change
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 Fall '07
 campion
 Atom, Atomic orbital, CH 301H Fall

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