[UPSC CSE 2024] Atomic Physics (Q13, 10+10=20M)

(i) Using free electron theory of metals, calculate the Fermi energy level of sodium atom at absolute zero. Assume that sodium has one free electron per atom and its density is 0\cdot 97\text{ gm/cm}^3. (ii) Draw the energy level diagram and mathematical expressions for the following : I. E_n of an electron confined in a one-dimensional box II. Linear harmonic oscillator Make a qualitative comparison of the above two cases.