786 18 The Electronic States of Atoms. II. The Zero-Order Approximation for Multielectron Atomsconfiguration (1s)^2 (2s)^2 (2p)^3. Use the Slater determi-
nant notation. How many terms are in the wave function
written as a sum of terms without determinant notation?
18.24Find the possible term symbols for the lowest-energy
configuration of the chlorine atom. Use the fact that a
subshell withnempty spin orbitals gives the same terms
as one withnfilled spin orbitals.
18.25Find the possible term symbols for the following atoms in
the given configurations:
a.C(1s)^2 (2s)^2 (2p)^2
b.Se(1s)^2 (2s)^2 (2p)^6 (3s)^2 (3p)^6 (4s)^2 (3d)^10 (4p)^4
18.26Find the possible term symbols for the following atoms in
the given configurations:
a.Ar(1s)^2 (2s)^2 (2p)^6 (3s)^2 (3p)^6
b.Mg(1s)^2 (2s)^2 (2p)^6 (3s)^218.27Find the possible term symbols for each of the following
configurations of the Be atom:
a.(1s)^2 (2s)^2
b.(1s)^2 (2s)(3s)
c.(1s)(2s)(3s)(4s)
18.28Find the possible term symbols for:
a.Li(1s)^2 (2s) configuration
b.F(1s)^2 (2s)^2 (2p)^5 configuration
c.Mg(1s)^2 (2s)^2 (2p)^6 (3s)^2 configuration
18.29Tell how many states correspond to each of the following
terms (include all possible values ofJ):
a.^3 D
b.^4 F
c.^2 SSummary of the Chapter
In the “zero-order” approximation, the repulsions between electrons are neglected.
The energy eigenfunctions of a multielectron atom are products of one hydrogen-like
spin orbital for each electron, and the energy eigenvalues are the sum of the orbital
energies. The wave functions must be antisymmetrized to conform to the physical
indistinguishability of the electrons. This leads to the Pauli exclusion principle, which
states that no two spin orbitals in any orbital wave function can be the same function.
Orbital and spin angular momentum values for various electron configurations can be
determined, and Russell–Saunders term symbols can be used to specify the energy
levels corresponding to these values.ADDITIONAL PROBLEMS
18.30For the beryllium atom, Be:
a.Write the Hamiltonian operator, assuming a stationary
nucleus.
b.Write the zero-order Hamiltonian operator (excluding
the electron–electron repulsion terms).
c.Write the ground-state wave function in the simple
orbital approximation, without antisymmetrization.
d.Write the antisymmetrized ground-state wave function
as a Slater determinant.
e.Consider the ground-state configuration (1s)^2 (2s)^2.
Determine the values ofS,L,ML, andMSthat can
occur. Write the Russell–Saunders term symbols for all
terms that can occur.
f. Consider the subshell configuration (1s)^2 (2s)(2p).
Determine the values ofS,L,ML, andMSthat can
occur. Write the Russell–Saunders term symbols for all
terms that can occur.
g.Consider the subshell configuration (1s)^2 (2p)(3p).
Determine the values ofS,L,ML, andMSthat can
occur. Write the Russell–Saunders term symbols for all
terms that can occur.
18.31From the pattern of nodal surfaces observed in the
subshells that we have discussed, predict the following: