Section
I. Use the uncertainty principle to estimate the ground state energy of a linear harmonic oscillator.
Given that (sigma)x, (sigma)y,(sigma)z are Pauli spin operators, prove the following relationships
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Consider the one dimensional wavefunction

sie(x) Axe

Calculate A so that sie(x) is normalized.
Using Schrodinger's equation find the potential and energy E for which sie(x) is an eigenfunction. (Assume that as
Sodium doublets are produced by transitions

<img src='./qimages/197-1d.jpg'>
Calculate the Lande g-factors for these levels.


Why should rotational Raman spectrum show a separation of the first Raman line from the exciting line equal to 6B while the separation between successive lines equals to 4B cm- where B is the rotational constant?

2. Solve the radial part of the time-independent Schrodinger equation for a hydrogen atom. Obtain an expression for the energy eigenvalues.

What is the degree of degeneracy of the energy eigenvalues What happens if the spin of the electron is taken into account?
3. When a nucleus with spin f is subjected to magnetic field, how does the energy level split and what will be the energy of separation between any two adjacent levels Estimate the spin-lattice relaxation time in terms of transition probability for a nucleus with spin
Why should proton chemical shift in CH3 CHO occur when it is subjected to a magnetic field


4. What will happen to the energy level of an unpaired electron when subjected to an external magnetic field Find the condition for electron spin resonance.
Describe the vibra!ion-rntation spectra of a polyatomic linear molecnle. What are Q and R branches Draw rotational energy levels of the vibrational stales v 0 and v 1 and perpendicular vibrational-rotational transitions of a linear polyatomic molecule.

Section
5. Determine from the given data whether the
following reactions are exothermic or endothermic:
<img src='./qimages/197-5a.jpg'>


Calculate the recoil energy of 5726Fe nucleus when it emits a gamma photon of energy 14 keV.
Which of the fol lowing reactions are.permitted or forbidden by various conservation laws
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<img src='./qimages/197-5c1.jpg'>

Metallic iron undergoes a structural phase transition from bee to fee at 910(degrees)C. At this temperature, the atomic radii of iron atoms in the bee and fee structures are 0.126 x 10-9 m and 0.129 x 10-9 m respectively. Calculate the volume change in percentage during this structural change.
What are the rules followed in biasing a bipolar junction transistor when it is used as an amplifier Show how and transistors to be used as an amplifier are biased and the direction of flow of base, collector and emitter currents.
6. Write down the Bethe-Weizsiicker semiempirical mass formula for a nucleus. Explain the significance of each term occurring in it. Discuss the stability of a nucleus against /3(beta)-decay. What is the effect of pairing term on stability

What are mirror nuclei? How does the charge independence of nuclear force emerge from this concept
7. Starting from an expression for the group velocity, arrive at an expression for the effective mass of an electron in a semiconductor. Explain the significance of sign of the effective mass.
Classify diamagnetic, paramagnetic and ferromagnetic materials in terms of their magnetic susceptibility sie). Plot and explain the variation of with temperature for the three materials.
Explain the variation of magnetisation of a type-I and type-II superconductors as a function of applied magnetic field.

8. Construct an operational amplifier based analog computer to solve the differential equation
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Construct an operational amplifier based analog computer to solve the differential equation
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