Generate the group multiplication table for the water molecule.
The water molecule (H₂O) has a C₂v point group, which includes the following symmetry operations: the identity operation (E), two vertical mirror planes (σv and σ'v), and a twofold rotation axis (C₂). To generate _______ ____ ____ _______ ______ ________ _____.
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Calculate the energy of the first excited state of an electron confined to a one-dimensional box with . (3 + 2 = 5 marks)
(b) Define degeneracy and calculate the degeneracies of the first five energy levels for a particle of mass confined to a cubic box of edge length
.
Derive the expression for the rotational energy levels of a rigid rotor.
Justify the statement: "The average distance of the electron in the ground state of hydrogen atom is more than its most probable distance in the same state."
Calculate the wavelength of light emitted when an electron in a helium ion () transitions from
to
. (3 + 2 = 5 marks)
(b) Evaluate and
, and discuss the significance of the results.
Define the perturbation method. Formulate an expression for the energy of a helium atom considering electron-electron repulsion as a first-order perturbation.
Why is the energy level expression for hydrogen-like atoms modified in multi-electron atoms?
Compare the treatment of ionic terms in Valence Bond Theory (VBT) and Molecular Orbital Theory (MOT) for the hydrogen molecule.