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http://ocw.mit.edu 5.80 Small-Molecule Spectroscopy and Dynamics
1. In the spectrum of rubidium, an alkali metal, the short-wavelength limit of the diﬀuse series is
4775 Å. The lines of the ﬁrst doublet in the principal series (52 P3/2 → 52 S 1/2 and 52 P1/2 → 52 S 1/2 )
have wavelengths of 7800 Å and 7947 Å, respectively.
(a) By means of term symbols, write a general expression for the doublets of the sharp series,
giving explicitly the possible values for n, the principal quantum number.
(b) What is the spacing in cm−1 of the ﬁrst doublet in the sharp series?
(c) Compute the ﬁrst ionization potential of rubidium in cm−1 and electron-volts (eV).
2. In the ﬁrst transition row of the Periodic Table there is a regular trend in ground-state multiplicities
from calcium (singlet) to manganese (sextet) to zinc (singlet), with one exception.
(a) Why does the multiplicity rise to a maximum and then fall?
(b) Explain the discontinuity shown by chromium (atomic number 24).
(c) Niobium, the element under vanadium in the second transition row, also shows a discontinuity
in multiplicity, though vanadium does not. Explain.
3. Atomic eigenfunctions contain a factor exp(iM φ). When the atom is a magnetic ﬁeld B, the quantum
number M represents the projection of the J –vector on B (− J ≤ M ≤ + J ). The usual selection rules
for L, S , and J still hold for moderate B, and in addition a selection rule governing the values of
Δ M becomes important. The dipole-moment operators for transitions involving M are ce�� and
c� e�⊥ cos φ. The coeﬃcients c and c� are non-zero constants (for the purposes of this problem); e
is the charge on the electron; and �� and �⊥ are the components of the electric ﬁeld of the radiation
parallel and perpendicular to B. Derive the selection rules for Δ M for radiation polarized parallel
and perpendicular to B.
4. Calculate the Zeeman pattern to be expected for the sodium D–lines at 10,000 gauss (G). You may
neglect nuclear hyperﬁne interactions. Indicate the polarization of each Zeeman line, that is, whether
the electric vector of the emitted radiation is parallel to the applied magnetic ﬁeld (π–component) or
perpendicular to it (σ–component). (a) Show qualitatively the Stark eﬀect to be expected for the sodium D–lines. The splittings are
proportional to what power of the electric ﬁeld strength?
(b) What do you think might happen to a beam of ground-state sodium atoms passing through a
strong inhomogeneous magnetic ﬁeld? a strong inhomogeneous electric ﬁeld?
5. An atom is in a (2 p)2 3 Po state.
A. List all of the L−S terms to which an electric dipole allowed transition might occur. Specify J
values and whether the state must have a o right superscript.
B. List all two electron conﬁgurations to which allowed transitions occur.
6. A new superheavy element, Dk or Dreckium, has recently been discovered. Its atomic number is
120 and it is in Group IIA of the periodic table. The following Dk I spectral lines have been observed
(relative intensities in parentheses):
in absorption at
(1600) Additional lines observed in emission include (many others are omitted from this table)
and a group of 6 lines with relative intensities quite diﬀerent from those observed in absorption. The
emission intensities for these 6 lines are included in the table of absorption lines. (a) Assign the observed spectra and construct an energy level diagram. You should make use of
all the tricks used by spectroscopists:
(i) Search for repeated frequency intervals;
(ii) Search for progressions described by A − B/n2 where A and B are constants and n is the
principal quantum number;
(iii) Take advantage of relative intensity information, especially temperature dependent inten
(iv) Analogies with other group IIA atomic spectra;
(v) Hund’s rules;
(vi) The Land´ interval rule.
You should also assume that I have not included any misleading information such as lines be
longing to another atom or to Dk II, transitions in which the lower level does not belong to
one of the three predicted low-lying conﬁgurations involving 8 s, 8 p, and 7d orbitals, or transi
tions involving signiﬁcantly perturbed levels. Atomic spectroscopists should be so fortunate!
Because Dk is a heavy atom, there is at least one (weak) intercombination transition.
(b) Can you explain why the lines 20179, 19901, and 19484 cm−1 exhibit intensity enhancements
in emission at high pressure and in regions of a discharge in which large electric potential
gradients exist? ...
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