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10 Nov 2019
III-2. Shell Model for Many-Electron Atoms (Oxtoby 5.2) 51 Shell Model for Man ectron Atoms: X-Ra (Some of you commented on the midterm survey that you wish to see powerful applications of quantum chemistry. This exercise is to honor those students.) Although there is no analytical solution to the TISE (time-independent Schrodinger equation) of any many- electron atom, one can still borrow the concepts and results from the H-atom, a one-electron atom, to gain some qualitative understanding. For example, in the so-called "Hartree model" or "shell model", we single out an electron, and enclose the nucleus and the rest of electrons to form a core. Then we use the H-atom formula to calculate the energy of this single-out electron X-ray is generated by a Coolidge tube (figure right), invented by William Coolidge in 1913. In the Coolidge tube, the electrons are produced by thermionic effect from a tungsten (W) filament heated by an electric current. The filament is the cathode of the tube. The high voltage potential is between the cathode and the anode, the electrons are thus accelerated, and then hit the anode. The anode is usually made out of tungsten or molybdenum (Mo, Z-42). Please predict the frequency of the X-ray released by the 2p - 1s transition by Mo. Assume the effective charge experienced by the 1s or 2p electron in Mo is the full un-shielded nuclear charge
III-2. Shell Model for Many-Electron Atoms (Oxtoby 5.2) 51 Shell Model for Man ectron Atoms: X-Ra (Some of you commented on the midterm survey that you wish to see powerful applications of quantum chemistry. This exercise is to honor those students.) Although there is no analytical solution to the TISE (time-independent Schrodinger equation) of any many- electron atom, one can still borrow the concepts and results from the H-atom, a one-electron atom, to gain some qualitative understanding. For example, in the so-called "Hartree model" or "shell model", we single out an electron, and enclose the nucleus and the rest of electrons to form a core. Then we use the H-atom formula to calculate the energy of this single-out electron X-ray is generated by a Coolidge tube (figure right), invented by William Coolidge in 1913. In the Coolidge tube, the electrons are produced by thermionic effect from a tungsten (W) filament heated by an electric current. The filament is the cathode of the tube. The high voltage potential is between the cathode and the anode, the electrons are thus accelerated, and then hit the anode. The anode is usually made out of tungsten or molybdenum (Mo, Z-42). Please predict the frequency of the X-ray released by the 2p - 1s transition by Mo. Assume the effective charge experienced by the 1s or 2p electron in Mo is the full un-shielded nuclear charge
Casey DurganLv2
12 Oct 2019