141: CHEM Problem Set 8
(60 pts) Due by noon Wednesday, Nov 18, 2009
1) (8 pts) Hot objects can emit blackbody radiation that appears red, orange, white, or bluish-white, but never green. Provide a rationalization.
2) (8 pts) Vast clouds of luminous hydrogen gas have been found in interstellar space. Spectroscopic evidence suggests that the atoms are very hot and atoms in excited states with n 100 are not uncommon. a) What wavelength of light would be detected if some of the atoms decayed from the n = 100 level to the n = 2 level? b) To which spectroscopic series of the hydrogen atom would this transition be assigned? c) Would a transition from n = 110 to n = 100 occur at a longer or a shorter wavelength than those found for the Balmer series? 3) (8 pts) Gilbert, Kirss, Foster, and Davies, chapter 7, exercise 7.54, pg. 351. 4) (6 pts) The velocity of the electron in the Bohr model of the atom was given in terms of known constants, the nuclear charge Z, and the quantum number n on pg 146 of the lecture handouts. Calculate the velocities of the electrons in the ground state of a He+ ion and in the ground state of a U91+ ion. Compare these velocities to the speed of light. As the velocity of an object approaches the speed of light, relativistic effects become important. which In kinds of atoms do you expect relativistic effects to be greatest? 5) (15 pts) Draw two-dimensional cross sectional representations for the following wavefunctions of the hydrogen atom. Include the x, y, and/or z axes, if necessary, to define the orientation in space. Be sure to clearly label the signs and the nodes. a) 2pz b) 3pz c) 3dx2-y2 d) 3dxz e) 4 s
6) (6 pts) Gilbert, Kirss, Foster, and Davies, chapter 7, exercise 7.84, pg. 352. For each of the allowed combinations, name the type of orbital it describes (e.g., 1s, 3p, etc.). For the combinations that are not allowed, indicate why they are not allowed.
-OVER-
7) (9 pts) Atoms or molecules which have one or more unpaired electrons are called paramagnetic and are attracted by magnetic fields. Atoms (or molecules) in which all electrons are paired are called diamagnetic and are weakly repelled by magnets. a) On the basis of their ground state electronic configurations, indicate which of the following ions are expected to be paramagnetic and which should be diamagnetic: Li_, B+, O_, Al3+, S2-, Ar+, Se+, and Te_. b) Considering only the ground state electron configurations of neutral atoms across the periodic table, why are there more elements that have paramagnetic atoms than have diamagnetic atoms?