Question

(i) Derive a generic relationship between the separation of vibrational energy levels, ΔG, and the vibrational quantum number for an arbitrary transition from v to v + 1. [3 marks]

(ii) What factors influence the strength of transitions between two, bound electronic states of a molecule? [3 marks]

(iii) Explain why the rotational constant is different for different vibrational energy levels. A diagram may be helpful. [3 marks]

(iv) Use a diagram to show differences between the experimental measurement of an absorption spectrum and a Raman spectrum? [4 marks]

(v) The solution to the Schrödinger equation for the hydrogen atom results in several quantum numbers. Give the name, symbol, and the physical significance of these quantum numbers, along with the range of their values.

Answer 1

3) every vibrational levels have different frequency of stretching and thus will have different net bond length (r). Bond length (r) will vary, then B will also vary.

5) n= principle quantum number : it signifies the main shell where electron belongs

l= (0,1,....n) : azimuthal quantum number : it represents the subshell and the orbital whwre the electron belongs.

m( -l,...,0,....l) magnetic quantum number: it represents the orientation of electron in space.

s( -1/2 or 1/2) spin quantum number: it shows whether the electron top is spinning in upward direction or downward direction.