Prove that the Schrödinger’s equation is not valid for many-electron systems.
Prove that the Schrödinger’s equation is not valid for many-electron systems.
Consider Schrödinger’s time-dependent equation for an electron, with a potential that is uniform and constant at a value Vo, with a solution of the form exp[i(kz−ωt)]. Deduce the relationship giving k in terms of ω and Vo , and deduce under what conditions there is a solution for real k.
1. The “particle in the box” problem uses simplifications that allow us to treat Schrödinger’s equation without the use of computers. a. List these assumptions and show how they simplify the applications of the Hamiltonian operator. b. Why aren’t d subshells found in the second shell? c. Why are there seven f atomic orbitals in an f subshell? d. What are possible combinations of the four quantum numbers for an electron in 5f atomic orbitals?
Two-electron system. (A) Which of the following are physically valid wavefunctions for a two-electron system such as the He atom or the H2 molecule? (B) What property makes them physically valic wavefunctions? (a) y(12)-1s(1)a(1) . 1s(2)A(2) (c) Ψ(1,2)-Isa(1)IsE(2)-1sa(2)1sE(1). Multi-electron atom. Consider a sodium cation, Nat. (A) How many variables does the multi-electron wavefunction describing its ground state depend on? (B) How many kinetic-energy, repulsion and attraction terms are in the associated Hamiltonian?
Two-electron system. (A) Which of the following are...
8-2 Schrodinger’s wave equation applied very well to one electron systems such as hydrogen. What additions did it need to be applicable to multielectron systems and what did each addition do?. 8-3 Holding the number of electrons in an atom constant, what happens when the charge on the atom is increased?
A) What is the central reason why Schrodinger equation for the multi-electron systems cannot be solved without an approximation? B) List and provide brief, yet specific, information about 4 approximation methods for multi-electron systems.
A) What is the central reason why Schrodinger equation for the multi-electron systems cannot be solved without an approximation? B) List and provide brief, yet specific, information about 4 approximation methods for multi-electron systems.
Valid and invalid arguments expressed in logical notation. Indicate whether the argument is valid or invalid. Prove using a truth table. • p → q q → p —— ∴¬q • p → q ¬p —— ∴¬q
Prove that the given argument is valid. First find the form of the argument by defining predicates and expressing the hypotheses and the conclusion using the predicates. Then use the rules of inference to prove that the form is valid. (a) The domain is the set of musicians in an orchestra. Everyone practices hard or plays badly (or both). Someone does not practice hard. ------------------------------------------------------------ ∴ Someone plays badly.
(a) Is this boolean equation valid or invalid for all possible values of x,y and z? x XOR (y OR z) = (x XOR y) OR (x XOR z) (b) Prove your answer, by using a truth table
Identify which sets of quantum numbers are valid for an electron. Each set is ordered (n, l , ml, ms,)
Identity which sets of quantum numbers are valid for an electron. Each sot is ordered (n, l, ml mi). Check all that apply.