ChE 554
E Term 2020
HW 2
Due:
Sunday May 31, 11:59 pm
1.
Answer the following questions.
a.
Explain the failings of classical mechanics in describing/modeling atoms,
electrons, and molecules.
b.
Explain what the wavefunction of an atom/molecule is.
c.
Explain what an eigenvalue and eigenfunction are.
d.
Explain what the Hamiltonian operator is.
e.
Explain what a “particle in a box” is.
2.
Answer the following questions.
a.
Describe the experimental results that led to quantum mechanics.
b.
Describe how to get the measured value (e.g. temperature or momentum) from a
wavefunction.
c.
Explain what atomic units are.
d.
Explain why an electron around a proton nucleus doesn’t collapse into the nucleus.
3.
If
࠵? = ࠵?
$
࠵?
, find g for each of the following
࠵?
$
and f. Also indicate which solutions are an
eigenvalue/eigenfunction.
a.
࠵?
$
= ࠵?/࠵?࠵?
, f = cos(-x)
b.
࠵?
$
= ࠵?
)
/࠵?࠵?
)
, f = cos(-x)
c.
࠵?
$
= ( )
)
, f = sin(x)
d.
࠵?
$
= ࠵?࠵?࠵?
, f = ln(x)
4.
Write out the exact wavefunction for the 2p orbitals of a hydrogen atom. Draw/sketch the
electron density that would be derived from these wavefunctions.

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