Problem 5 (a) Two (unnormalized) excited state wavefunctions of the H atom are (1) 4 =...
The wave functions of the H-atom for the ground state and the first excited state are given by Yoo(θ, φ), 100(r' exp - , 200(r, θ, φ) a. Show that these 5 wave-functions are all mutually orthogonal to each other. b. Determine the expectation values(r2〉nl of the operator r2 defined as follows 〈r2〉10-rd3TV1,00(a) r2ψ1,0,0(2) and 〈r2〉20, 〈r2)21 defined analogously The wave functions of the H-atom for the ground state and the first excited state are given by Yoo(θ, φ), 100(r'...
The wave functions of the H-atom for the ground state and the first excited state are given by Yoo(θ, φ), 100(r' exp - , 200(r, θ, φ) a. Show that these 5 wave-functions are all mutually orthogonal to each other. b. Determine the expectation values(r2〉nl of the operator r2 defined as follows 〈r2〉10-rd3TV1,00(a) r2ψ1,0,0(2) and 〈r2〉20, 〈r2)21 defined analogously
Problem 4 Consider the hydrogenic wavefunctions Un,1,mi = Rn,l(r)Yı,mı (0,0) for an elec- tron in a hydrogen atom (Z = 1). The electron is in the 2s state. a) Determine the location of the radial node in terms of ao. b) Calculate the most probable radius of an electron in a 2s state, and com- pare this radius with the most probable radius of the ls state (ao). c) Using the formula provided in class, determine the mean radius for...
5. A particle in the harmonic oscillator potential has the initial wave function Psi(x, 0) = A[\psi_{0}(x) + \psi_{1}(x)] for some constant A. Here to and ₁ are the normalized ground state and the first excited state wavefunctions of the harmonic oscillator, respectively. (a) Normalize (r, 0). (b) Find the wavefunction (r, t) at a later time t and hence evaluate (x, t) 2. Leave your answers involving expressions in to and ₁. c) sing the following normalized expression of...
An electron in the Hydrogen atom is in the excited state with energy E2. a) According to the Bohr model, what is the radius of the atom in this state, in Angstroms? b) What is the wavelength le of the electron, in Angstroms? c) What is the momentum of the electron, in kg-m/s ? d) This atom decays from the excited state with energy E2 to the ground state with energy E1 . What is the energy of the emitted photon?...
The electron in a hydrogen atom is in the first excited state, when the electron acquires an additional 2.86 eV of energy. What is the quantum number of the state into which the electron moves? a. 1 b. 2 c. 3 d. 4 e. 5
A H-atom is in an excited state represented by a dot. What are the possible energies of emitted photons? 10.se -3.4ev -13.6V 0.65 eV, 0.85 eV 0.85 eV, 1.9eV 3.4 eV, 1.9 eV 1.9 eV, 10.2eV 1.9 eV, 10.2eV, 12.1eV QUESTION 2 3.4ev A 12.0 eV electron collides with an H-atom in its ground state. What is the energy of the electron after the collision? -13.6ev 12.0 eV 10.5 eV 8.6 eV 1.8 eV 1.6 eV QUESTION 3 A collection...
Part c and h please Help (a) Describe the essence of the orbital approximation. 3 pts (b) Suggest antisymmetrized wave functions of the Helium atom in the singlet (1s)2 ground state, and the (c) Normalize the (1s) wave function of (b), provided that individual space orbitals and spin functions are (d) Explain the energy ordering and degeneracy of the lowest three singlet and triplet states of the Helium singlet (1s) (2s) and triplet (1s)(2s) excited-state configurations in the orbital approximation....