CHE 2101C01 Mid-Semester Exam 2021 PDF

Department of Chemistry Mid-Semester Examinations Paper CHE 2101C01 Day & Date : Thursday, 07.01.2021 Time : 11.00am – 12.00noon Q1....

Department of Chemistry Mid-Semester Examinations Paper CHE 2101C01 Day & Date : Thursday, 07.01.2021 Time : 11.00am – 12.00noon Q1. (a) Define or explain Hermitian operator. 2πi.x/λ (b) If Ψ = A e , show px = (h/2πi)dΨ/dx (c) Show that [ ] =ih/2π (d) Write kinetic energy part of Hamiltonian operator Hop for H2 molecule (e) Write the wave function for particle in three dimensional box. (f) How many degeneracies are there in the three dimensional box when the energy of state 14h2/8ma2. (g) Butadiene contains 4π electrons, each of which moves freely in the molecule. Assume the molecule in a one-dimension box. The energy required to the transition of electron to the first excited state will be E = ---------- ? (h2/8ma2) b. (3h2/8ma2) c. (5h2/8ma2) d. (8h2/8ma2) e. none (h) For a particle in three dimensional box with Lx = Ly = Lz/3 =L. What’s the energy at the E111? OR Prove that the eigenvalues of a Hermitian operator are real. Q2 (a) Fill in the blanks : In case of heavy elements, the ________________ (spin-orbit /electrostatic) interaction is stronger than ______________ spin-orbit / electrostatic) interaction between them. (b) Consider the excited state transition 1s¹2p¹ → 1s¹3d¹ of a helium atom and answer the following related questions. (i) Find the number of microstates belonging to each of the configuration. (i) Derive the energy terms arising from the two configurations. [Hint : Each of the configuration will give rise to 2 energy terms] (ii) Find the spin-orbit energy states associated with each of the energy terms. (c) Give the significance of the nephelauxetic ratio β. (d) The Racah parameter B is 460 cm⁻¹ in [Co(CN)₆]³⁻ and 615 cm⁻¹ in [Co(NH₃)₆]³⁺. Explain the difference in the values of Racah parameter B. Q3. Explain the following statements in brief : (i) A linear relationship between formation constants of the complexes and protonation constants of the ligands is expected. (ii) Bipyridine ligand forms very stable complexes with the transition metal ions in their lower oxidation states. (iii) Glycine forms more stable complex than methylamine though the latter is more basic. (iv) Sidgwick’s type I metal ions prefer to bind with O- donor ligands than N- donor ligands. OR The class B metal ions prefer to bind with S- donor ligands than O- donor ligands. (v) The formation of chelates, results in stability due to favourable entropy change.