185

A short exercise designed to show how small a nucleus is relative to the
whole atom.

186

Another of Levine's very informative true/false questions.
Parts (c), (d), and (e) explore the differences between y, y^{2}, and y^{2}r^{2}dr
for the 1s orbital [n = 1, l = 0, and y = A_{1,0exp}(Zr/2a),
where a is a constant]. Remember that y
is the wave function, y^{2} is the square of the wave
function and y^{2}dt = y^{2}r^{2}sinqdqdfdr is what must be integrated to get the
probability. If there is no angular
dependence (and there is none for an s orbital) then y^{2}r^{2}sinqdqdfdr can be replaced by (4p)y^{2}r^{2}dr (where the factor 4p
isn’t often important). In simpler
problems (particle in a box, harmonic oscillator) dt is just dx, but for integrations over r in spherical polar coordinates
dt = (4p)r^{2}dr
if there is no angular dependence and is more complicated if there is angular
dependence.
Parts (h) and (i) refer to very common
misconceptions.

188

More true/false questions.
Part (a) asks if the allowed energy levels for an electron and a proton have
either E = (13.60 eV)/n^{2} or E ³
0. If E ³ 0 then the electron is
not interacting with the proton. That
situation is allowed, but most people would not refer to it as “an H atom”.
If E > 0 then the energy can have any value (i.e., there are no quantum effects).
Parts (b) and (c) explore an important distinction. Ionization means promotion of the electron
from a bound state to an unbound state (E ³ 0). If E ³ 0 there are no quantum
levels so that a photon of any
energy above the minimum can do the job.
For a transition between two bound levels the photon energy must match
the energy difference between the levels very exactly.

189

A short exercise about the quantum numbers of electrons in atoms.

1810

Another short exercise about the quantum numbers of electrons in
atoms. This exercise includes a
question about degeneracy.

1811

How does energy for a 1electron ion change with nuclear charge? The constant in the energy expression is 13.60 eV/electron.
One eV is equal to 96.485 kJ/mol and so is a very large unit.

1812

Calculate the frequency and wavelength for a transition of the electron in
an H atom. The constant in the energy
expression is 13.60 eV/electron.

1863

A review problem from calculus, but always worth doing again. Integrate the volume element for spherical
polar coordinates (r^{2}sinqdqdfdr)
to get the formula for the volume of a sphere [V = (4/3)pr^{3}]. The integration limits are 0 – r for r, 0 –
p
for q, and 0 – 2p
for f.



1848

A simple exercise in writing the Hamiltonian for a 3electron atom (i.e.,
for a Li atom). The idea is to see how
the problem gets complicated even if there are only three electrons. Imagine what the expression would look like
if there were 20 or 30 electrons.

1851

Write out the electron configurations for atoms with 1 to 10 electrons
remembering the rules taught in General Chemistry. How many unpaired electrons are there for
each atom? (If an atom or ion is
described a paramagnetic then it has unpaired electrons).

1852

A short problem very much like 1811.

1855

A kind of problem always asked in CHE 105.

1860

Another review problem from CHE 105.

1864

Another review problem from CHE 105.



(no number)

Show that the Hatom 1s and 2s
orbitals are orthogonal. Then do the
integration again leaving out the r^{2}
factor in the volume element to show that the integral without that factor is
not equal to zero. The wavefunctions are shown on pg. 641. It is safe to leave out the normalization
factors since the question is only whether the integral is zero or not. It is also safe to set Z equal to 1 (as it
is for an H atom). To do the integrals
it is necessary to use the following:
the integral from x = 0 to x = ¥ of x^{n}e^{ax}dx is n!/(a^{n+1})
if n is an integer >0 and a > 0, which they are in this case. Note that when the r^{2} factor is left out this formula cannot be used for
one of the two integrals (because n = 0) but that one integral is easy to
evaluate.

(no number)

Verify that there are four lines
in the visible spectrum (l in the range
400 – 700 nm) of an H atom. Then
calculate the upper and lower quantum numbers for the lines in the visible
spectrum of He^{+} (but not
for He). He^{+} has a nuclear
charge of 2.



1836

A set of T/F questions about
symmetric and antisymmetric functions.

1837

A second set of questions about functions
that are symmetric, antisymmetric, or neither. Please remember that most functions are
neither symmetric nor antisymmetric, just as most functions (e.g., an exponential or logarithmic
function) are neither even nor odd.

1838

A third set of questions about
functions that are symmetric, antisymmetric, or neither. Remember that for integers even*even=even,
even*odd=odd, and odd*odd=even;
similarly sym*sym=sym, sym*antisym=antisym, and antisym*antisym=sym.

1840

A short exercise in getting the
term symbol (eg,
^{3}P) given the name of the orbital occupied by the one electron
present. The problem does not ask for
the possible values of the quantum number describing the spinorbit coupling,
but it is simple to give these values because in this oneelectron system
they are just L+S and LS. (Of course
if either L or S = 0 there can be no spinorbit coupling). The value of this quantum number is given
as a subscript on the right of the term symbol (eg, ^{3}P_{2}).

1841

A simple exercise in turning the
term symbol into L and S values.

1844

A simple exercise designed to
emphasize that the electrons in filled subshells do not contribute to either
L or S, and that the value of the principal quantum number does not appear in
the term symbol. This problem really
just repeats the questions asked in 1840.
