## Module 1

Q1. Explain the effect of non-coulomb central potential on the electronic energy levels of an atom.

Q2. What is the ground state configuration of Ne.

Q3. What is the total degeneracy of the ground state of carbon.

Q4. Write one of the excited state configurations of nitrogen and calculate the degeneracy of the excited state.

Q5. Write the ground state configuration of Fe (Z = 26); Ru (Z = 44)  and Au (Z = 79). Discuss why it is different from K (Z = 19).

Q6. How many transition lines do you find for 2D  → 2P transition of Ca+ after L.S. splitting. Show the energy level diagram and transition also.

Q7. Same as Q.6 for 3P  → 3D.

Q8. Write the coupled function | j1 j2 j m> = | 3 2 4 3> as a linear combination of uncoupled functions | j1 j2 m1 m2> by calculating the appropriate Clebsch – Gorden coefficients.

Q9. Find out the terms arising from p2 and d2 configuration in j – j coupling scheme. Draw the relative energy level diagram and compare it with the relative energy level positions of the terms arising from L – S coupling.

Q10. Using ML – MS table, find out the terms arising from ppp configuration in LS coupling approximation.

Q11. Two angular momenta J1= 1 and J2= ½ are coupled to form a new angular momentum J. An operator V operates only on basis function | J1 m1> not on | J2 m2>. The values of the matrix elements of this operator in the uncoupled basis set | J1 m1> are as follows.
< J1= 1, m1 = 0| V | J1= 1, m1 = 0 > = 3/2

< J1= 1, m1 = 1| V | J1= 1, m1 = 1 > = ¾
< J1= 1, m1 = 0| V | J1= 1, m1 = 1 > = 3/5
< J1= 1, m1 = 1| V | J1= 1, m1 = 0 > = 3/5

Calculate the value of the matrix element < J= 1/2, M= 1/2| V | J= 1/2, M= 1/2 > .

Q12. The fine structure of 4D → 4P transition for C+ is recorded. The transitions corresponding to 4D3/24P5/2 , 4D5/24P5/2 and 4D1/24P3/2 are observed at 6812.2 Å, 6800.5 Å and 6798.0 Å respectively.
(a) Calculate the spin – orbit constants ( in cm-1) for 44D and 4P states.
(b) Show all other allowed transitions on energy level diagram and calculate their wavelength (in Å).

Q13. The normalized hydrogen atom ground state wave function is given by Ψ100(r) = (1/4π)1/2(z/a0)3/22exp(-zr/a0).
What is the ground state energy of Li+, according to independent particle model. Considering the electron – electron repulsion, calculate the ground state energy of Li+ according to first order perturbation theory.

Q14. The transition 2P1/22P1/2 for an atom A is at 5500 Å. The same transition for another atom B is at 5501 Å. Calculate the minimum magnetic field for which the photons emitted by atom A will be absorbed by atom B.

Q15. The chemical formula of a molecule is C4H10O. It produces the following NMR spectrum. Find out its chemical structure.

Q16.Calculating the splitting, obtain the Zeeman pattern for 2P3/22S1/2 transition.