BT-201 Engineering Physics - Jun 2023 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aState and prove (Elementary proof) Heisenberg's uncertainty principle.
   How to answer

   • Statement of Heisenberg's uncertainty principle
   • Mathematical formulation: $\Delta x \cdot \Delta p_x \ge \frac{\hbar}{2}$
   • Elementary derivation/proof using single-slit diffraction or gamma-ray microscope thought experiment
   • Physical significance and implications
2. 7 Marks
   bDerive time dependent and time independent Schrodinger wave equation.
   How to answer

   • Representation of plane matter wave function
   • Derivation of time-dependent Schrodinger equation by differentiation with respect to space and time
   • Separation of variables technique for time and space coordinates
   • Derivation of time-independent Schrodinger wave equation
3. 7 Marks
   aExplain the working principle of Mach-Zehnder interferometer with suitable ray diagram.
   How to answer

   • Ray diagram showing laser source, two beam splitters, two mirrors, and two detectors
   • Working principle based on division of amplitude
   • Path difference and phase shift calculation between the two arms
   • Applications of Mach-Zehnder interferometer
4. 7 Marks
   bExplain Rayleigh's criterion of resolution. Derive an expression for resolving power of a grating.
   How to answer

   • Statement and explanation of Rayleigh's criterion for resolution of spectral lines
   • Condition for just resolved, well resolved, and unresolved spectra
   • Mathematical derivation of resolving power for plane diffraction grating: $\frac{\lambda}{d\lambda} = nN$
   • Factors affecting the resolving power
5. 7 Marks
   aDraw and explain the V-I characteristic curve of P-N junction diode. Differentiate between Avalanche and Zener breakdown.
   How to answer

   • V-I characteristic curve of P-N junction diode showing forward and reverse bias regions
   • Explanation of knee voltage, forward current conduction, and reverse saturation current
   • Comparative table between Zener breakdown and Avalanche breakdown detailing mechanism, doping, voltage range, and temperature coefficient
6. 7 Marks
   bExplain Kronig Penney model for periodic potential. Write down the Schrodinger equation and discuss conclusion of this model.
   How to answer

   • Introduction to Kronig-Penney model: rectangular periodic potential wells representing crystal lattice
   • Formulation of Schrodinger equation in regions $0 < x < a$ and $-b < x < 0$
   • Application of Bloch's theorem and boundary conditions yielding $P \frac{\sin \alpha a}{\alpha a} + \cos \alpha a = \cos ka$
   • Conclusions: Formation of allowed energy bands and forbidden energy gaps (band gap)
7. 7 Marks
   aWhat is the working principle of an optical fibre? How light propagates through it? Define terms : Numerical aperture, Population inversion, V-number.
   How to answer

   • Working principle of optical fiber: Total Internal Reflection (TIR) with condition $n_1 > n_2$
   • Explanation of light propagation through core and cladding via multiple internal reflections
   • Definition and formula for Numerical Aperture: $\text{NA} = \sqrt{n_1^2 - n_2^2}$
   • Definition of Population Inversion in lasers ($N_2 > N_1$)
   • Definition and formula for V-number (normalized frequency parameter): $V = \frac{2\pi a}{\lambda}\text{NA}$
8. 7 Marks
   bExplain construction and working of $\text{CO}_2$ laser with suitable energy level diagram.
   How to answer

   • Construction details: discharge tube, gas mixture ($\text{CO}_2$, $\text{N}_2$, $\text{He}$), mirrors/resonator cavity
   • Modes of vibration of $\text{CO}_2$ molecule (symmetric stretch, bending, asymmetric stretch)
   • Energy level diagram showing resonant transfer from excited $\text{N}_2$ to $\text{CO}_2$
   • Lasing transitions ($10.6\;\mu\text{m}$ and $9.6\;\mu\text{m}$) and role of Helium in depopulation
9. 14 Marks
   Write short note on any two: a) Zener diode b) Newton's ring c) Intrinsic and Extrinsic semiconductor through Fermi level d) Solar cell
   How to answer

   • Zener diode: heavily doped p-n junction, reverse breakdown mechanism, voltage regulation application
   • Newton's rings: interference in thin air film of varying thickness formed by plano-convex lens and glass plate, fringe diameter formulas
   • Fermi level: position in intrinsic semiconductor (middle of band gap) vs. n-type and p-type extrinsic semiconductors, temperature dependence
   • Solar cell: photovoltaic effect, p-n junction structure, V-I characteristics, conversion of light to electrical energy
10. 7 Marks
    aState and prove equation of continuity. Explain its significance.
    How to answer

    • Statement of continuity equation based on law of conservation of charge
    • Derivation using divergence theorem: relating net current flow across closed surface to time rate of decrease of enclosed charge
    • Differential form: $\nabla \cdot \vec{J} + \frac{\partial \rho}{\partial t} = 0$
    • Physical significance in steady and time-varying electromagnetic fields
11. 7 Marks
    bDefine the electric field intensity. Find out the expression for electric intensity due to infinite line charge.
    How to answer

    • Definition and unit of electric field intensity: $\vec{E} = \frac{\vec{F}}{q_0}$
    • Application of Gauss's Law: choice of a cylindrical Gaussian surface of radius $r$ and length $l$
    • Evaluation of electric flux through the curved surface and flat end caps
    • Expression derivation: $E = \frac{\lambda}{2\pi \varepsilon_0 r}$
12. 7 Marks
    aExplain Hall effect. Derive expression for Hall coefficient and Hall angle.
    How to answer

    • Definition and explanation of Hall effect with schematic of semiconductor slab under transverse magnetic field
    • Balancing Lorentz force and electrostatic force: $e E_H = e v_d B$
    • Derivation of Hall coefficient: $R_H = \frac{E_y}{J_x B_z} = \frac{1}{n q}$
    • Derivation of Hall angle: $\tan \theta_H = \frac{E_H}{E_x} = \mu B$
13. 7 Marks
    bDefine wave function and state its properties. Derive energy and momentum operator.
    How to answer

    • Definition of wave function $\psi$ and physical interpretation ($|\psi|^2$ as probability density)
    • Properties/conditions for well-behaved wave function (single-valued, continuous, finite, square-integrable)
    • Derivation of momentum operator $\hat{p} = -i\hbar \nabla$ using plane wave $\psi = A e^{i(kx - \omega t)}$
    • Derivation of energy operator $\hat{E} = i\hbar \frac{\partial}{\partial t}$
14. 7 Marks
    aWhat is interference of light? Describe young's experiment and derive expression of fringe width.
    How to answer

    • Definition of interference of light and conditions for sustained interference
    • Experimental setup of Young's double slit experiment
    • Derivation of path difference $\Delta = \frac{yd}{D}$
    • Conditions for maxima and minima
    • Expression for fringe width: $\beta = \frac{\lambda D}{d}$
15. 7 Marks
    bWrite down the difference between spontaneous and stimulated emission. Write down the applications of laser.
    How to answer

    • Table comparing spontaneous emission vs. stimulated emission on coherence, phase, directionality, and dependence on external radiation
    • Transitions and photon characteristics for both processes
    • Major practical applications of lasers in medicine, communication, industry, and scientific research