Comments re Chapter 18 Problems:

18-5

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

18-6

Another of Levine's very informative true/false questions.
Parts (c), (d), and (e) explore the differences between y, y2, and y2r2dr for the 1s orbital [n = 1, l = 0, and y = A1,0exp(-Zr/2a), where a is a constant].  Remember that y is the wave function, y2 is the square of the wave function and y2dt = y2r2sinqdqdfdr is what must be integrated to get the probability.  If there is no angular dependence (and there is none for an s orbital) then y2r2sinqdqdfdr can be replaced by (4p)y2r2dr (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)r2dr if there is no angular dependence and is more complicated if there is angular dependence.
Parts (h) and (i) refer to very common misconceptions.

18-8

More true/false questions.
Part (a) asks if the allowed energy levels for an electron and a proton have either E = -(13.60 eV)/n2 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.

18-9

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

18-10

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

18-11

How does energy for a 1-electron 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.

18-12

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.

18-63

A review problem from calculus, but always worth doing again.  Integrate the volume element for spherical polar coordinates (r2sinqdqdfdr) to get the formula for the volume of a sphere [V = (4/3)pr3].  The integration limits are 0 – r for r, 0 – p for q, and 0 – 2p for f.

 

 

18-48

A simple exercise in writing the Hamiltonian for a 3-electron 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.

18-51

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).

18-52

A short problem very much like 18-11.

18-55

A kind of problem always asked in CHE 105.

18-60

Another review problem from CHE 105.

18-64

Another review problem from CHE 105.

 

 

(no number)

Show that the H-atom 1s and 2s orbitals are orthogonal.  Then do the integration again leaving out the r2 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 xne-axdx is n!/(an+1)

if n is an integer >0 and a > 0, which they are in this case.  Note that when the r2 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.

 

 

18-36

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

18-37

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.

18-38

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.

18-40

A short exercise in getting the term symbol (eg, 3P) 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 spin-orbit coupling, but it is simple to give these values because in this one-electron system they are just L+S and L-S.  (Of course if either L or S = 0 there can be no spin-orbit coupling).  The value of this quantum number is given as a subscript on the right of the term symbol (eg, 3P2).

18-41

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

18-44

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 18-40.

 

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