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ILUULLUHUJJ. U TILI JL CUILIUI " J.. 3) Two-electron system: Consider a two-electron system. The spin-orbitals...
à 154 5. The example in question 4 was for a singlet state, which use spin...
à 154 5. The example in question 4 was for a singlet state, which use spin 20 2px 2px 2pz wavefunctions to impart the antisymmetry property. For triplets, the This is a 1812s1 "space" wavefunctions are used to enforce the antisymmetry triplet state property. For example, the proper antisymmetric wavefunction for a 2s'1s1 spinup-spinup configuration is: (1.2) - 92s(r.)41s(2) – 42s (r2)4s(r)) 2)915}a(1)a(2) V2 2px 2py 2pz a. Let's see what happens if the two electrons are in the same...
Quantum Mechanics II, 'Quantum Mechanics', David H. McIntyre 3. Consider two identical linear oscillators with spring...
Quantum Mechanics II, 'Quantum Mechanics', David H. McIntyre
3. Consider two identical linear oscillators with spring constant k. The Hamiltonian is ha d k (2 + x) H 1 + + 122, 2m d. 2 where x1 and 22 are oscillator variable. (a) by changing the variables 11 = x +, 19=xY find the energies of the three lowest states of this system? (b) If the particle are with spin 1/2, which of the above three states are triplet states...
3) Rank the following orbitals in order of increasing energy: 3s, 2s, 2p, 4s, 3p, ls,...
3) Rank the following orbitals in order of increasing energy: 3s, 2s, 2p, 4s, 3p, ls, and 3d. 4) How many orbitals in an atom can have the following quantum number or designation? a. 3p_ b. 7s c. 4p. d. 5d . e. 5f f. n=5 5) Answer the following questions by filling in the space: a) The quantum number n describes the of an atomic orbital. b) The shape of an atomic orbital is given by the quantum number...
5. [25 pts total Consider the H-atom system of an electron freely moving about a nu...
5. [25 pts total Consider the H-atom system of an electron freely moving about a nu When solve, looking at this system in spherical coordinates we obtain three differential equations to representing the radial distance (r), axial angle (θ), and azimuthal angle (d) coo rdinates. a) 12 pts] What is the approximation typically invoked to treat this system as just the behavior of the electron motion? Why is it acceptable to do so? b) [3 pts] Sketch a representation of...
A system consists of two particles of mass mi and m2 interacting with an interaction potential...
A system consists of two particles of mass mi and m2 interacting with an interaction potential V(r) that depends only on the relative distancer- Iri-r2l between the particles, where r- (ri,/i,21) and r2 22,ひ2,22 are the coordinates of the two particles in three dimensions (3D) (a) /3 pointsl Show that for such an interaction potential, the Hamiltonian of the system H- am▽ri _ 2m2 ▽22 + V(r) can be, put in the form 2M where ▽ and ▽ are the...
Problem Set 4 Atomic Structure and the Periodic Table Name: Date: Lab Section: General Instructions Complete the f...
Problem Set 4 Atomic Structure and the Periodic Table Name: Date: Lab Section: General Instructions Complete the following problems. Attach another sheet to give yourself space for problems 8,9,10 as needed. Assignment is due at the end of the lab period unless stated otherwise by instructor. 1.) Energy Levels and Sublevels for the Polyelectronic Atom (a) How many sublevels exist in the energy level (n = 5)? (b) How many orbitals exist in any f-sublevel? (c) What is the maximum...
à 154 5. The example in question 4 was for a singlet state, which use spin 20 2px 2px 2pz wavefunctions to impart the antisymmetry property. For triplets, the This is a 1812s1 "space" wavefunctions are used to enforce the antisymmetry triplet state property. For example, the proper antisymmetric wavefunction for a 2s'1s1 spinup-spinup configuration is: (1.2) - 92s(r.)41s(2) – 42s (r2)4s(r)) 2)915}a(1)a(2) V2 2px 2py 2pz a. Let's see what happens if the two electrons are in the same...
Quantum Mechanics II, 'Quantum Mechanics', David H. McIntyre
3. Consider two identical linear oscillators with spring constant k. The Hamiltonian is ha d k (2 + x) H 1 + + 122, 2m d. 2 where x1 and 22 are oscillator variable. (a) by changing the variables 11 = x +, 19=xY find the energies of the three lowest states of this system? (b) If the particle are with spin 1/2, which of the above three states are triplet states...
3) Rank the following orbitals in order of increasing energy: 3s, 2s, 2p, 4s, 3p, ls, and 3d. 4) How many orbitals in an atom can have the following quantum number or designation? a. 3p_ b. 7s c. 4p. d. 5d . e. 5f f. n=5 5) Answer the following questions by filling in the space: a) The quantum number n describes the of an atomic orbital. b) The shape of an atomic orbital is given by the quantum number...
5. [25 pts total Consider the H-atom system of an electron freely moving about a nu When solve, looking at this system in spherical coordinates we obtain three differential equations to representing the radial distance (r), axial angle (θ), and azimuthal angle (d) coo rdinates. a) 12 pts] What is the approximation typically invoked to treat this system as just the behavior of the electron motion? Why is it acceptable to do so? b) [3 pts] Sketch a representation of...
A system consists of two particles of mass mi and m2 interacting with an interaction potential V(r) that depends only on the relative distancer- Iri-r2l between the particles, where r- (ri,/i,21) and r2 22,ひ2,22 are the coordinates of the two particles in three dimensions (3D) (a) /3 pointsl Show that for such an interaction potential, the Hamiltonian of the system H- am▽ri _ 2m2 ▽22 + V(r) can be, put in the form 2M where ▽ and ▽ are the...
Problem Set 4 Atomic Structure and the Periodic Table Name: Date: Lab Section: General Instructions Complete the following problems. Attach another sheet to give yourself space for problems 8,9,10 as needed. Assignment is due at the end of the lab period unless stated otherwise by instructor. 1.) Energy Levels and Sublevels for the Polyelectronic Atom (a) How many sublevels exist in the energy level (n = 5)? (b) How many orbitals exist in any f-sublevel? (c) What is the maximum...
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