Question

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. 4 pts orthonormal ('orthonormal means orthogonal and normalized). 13 pts) atom. Describe how spin indirectly influences the energy of the wave funetions. |5 pts Given the following space part of an approximate wave function for the Li+ ion: (e) Write a physically possible spin part for this wave function. 13 pts :'() 2018 R. M. van der Vien (1) What energy would this state have if the 1/riz electron repulsion term in H did not exist? Express your (g) Describe qualitative how and why the energy of the state changes if the 1/ria term in is included. 13 (h) Determine the eigenvalue of the total spin angular moment um operator squared for the Lit ion in the (0) Define Hund's rule and justify it on the basis of the antisymmetry condition for fermion wave functions answer in units of Ry (Rydberg). |4 pts) pts) state described by equation (2), including the spin part determined in (e). 3 pts 14 pt 1

Answer 1

Normalized wave function in orbital approximation For triplet (1s) (2s) state of helium atom Psi(r, sigma_1, r_2 sigma_2) 1/squareroot 2 A[Psi_1s (r, alpha) Psi_2s (r_2 alpha)] = 1/squareroot 2 (Psi_1s (r_1) alpha (1) Psi_2s (r_2) alpha(2) - Psi_1s (r_2) alpha (2) Psi_2s (r_1) alpha (1)) = 1/squareroot 2 (Psi_1s (r_1) Psi_2s (r_2) - Psi_2s (r_1) Psi_1s (r_2) alpha (1) alpha(2)) For singlet (1s)^2 state of helium atom orthonormal Psi(r_1 sigma_1 - r_2 sigma_2) = 1/squareroot 2 A [Psi_1s (r, alpha) Psi_1s (r_2 beta)] = 1/squareroot 2 (Psi_1s (r_1) alpha (1) Psi_1s (r_2) beta(2) - Psi_1s (r_2) alpha(2) Psi_1s (r_1) beta (1)) = Psi_1s (r_1) Psi_1s (r_2) 1/squareroot 2 (alpha (1) beta(2) - beta (1) alpha(2)) \r\n Spin operator s^2 (1) alpha(1) = 1/2 (1/2 + 1) h^2 alpha (1) s^2 (1) beta(1) = 1/2 (1/2 + 1) h^2 beta (1) Spin of singlet s^2 {alpha (1) beta(2) - beta(1) alpha(2)} = 0(0 + 1)h^2 {alpha (1) beta(2)