Unformatted text preview: he quantum state of an electron in 3D (including spin)? l) (2 pts) What are the spatial quantum numbers for the atomic wavefunctions in a hydrogen atom? 8 of 20 m) (4 pts) Sketch probability isosurfaces for the three 2p wavefunctions (2px, 2py, and 2pz) for a hydrogenic atom in 3D (i.e. the shape of the orbitals). Label all axes. n) (3 pts) Sketch the potential V(r) for the hydrogenic atom. Draw in the energy levels En for the wavefunctions with l=0 (s orbitals). o) (2 pts) Write out the volume integral over all space of a function f(r, ) in spherical coordinates. 9 of 20 p) (6 pts) Calculate the expectation value of the radius (<r>) for the 1s wavefunction of a hydrogenic atom in terms of the Bohr radius ao. The 1s wavefunction is given by: ,, 1 1 √ Some or all of these integrals may be helpful: 4 exp exp
exp Write out the expressions you are using to solve this for full credit 10 of 20 q) (1 pts) What does the result from part g tell us? (15 words or fewer) r) (2 pts) Is the total energy E positive, equal to 0, or negative for an electron that has been ionized from an atom? s) (3 pts) For Z=2 (Helium), what are E1 and E3 in eV within the hydrogenic model? 11 of 20 t) (3 pts) Write out the electron configuration of an isolated atom of nitrogen (atomic # Z = 7) 12 of 20 2009 Exam 2, Problem 2 – Transitions Between Quantum States h) (3 pts) Imagine an electron in a 3D infinite square well with sides of length L (a cube of side L with infinite potential outside of the cube). Write out the formula for the energy of a state with nx, ny, nz. i) (5 pts) Write out a formula for the wavelength of a photon emitted when an electron makes a transition from a higher energy state with to a lower energy state. Use nx, ny, nz as quantum numbers for the lower energy state and mx, my, mz as quantum numbers for the higher energy state. 13 of 20 j) (4 pts) What is the wavelength of a photon emitted when an electron in the (mx, my, mz) = (3, 2, 1) state transitions to the ground state (lowest energy state) if L=1 nm? k) (4 pts) Sketch the...
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- Spring '14
- Frequency, pts