JNTU
JNTU B.Tech I APPLIED PHYSICS Previous Question Paper (September/October - 2021 - R18)
Answer any five questions. All questions carry equal marks.
Main
Show that the energies of a particle in a one dimensional potential box are quantized.
Answer
Consider a particle of mass m in a one-dimensional potential box of width a, where the potential V(x) = 0 for 0 ≤ x ≤ a and V(x) = ∞ elsewhere. The time-independent Schrödinger equation inside the box is:
Let k2 = 2mE/ℏ2. The general solution is ψ(x) = A sin(kx) + B cos(kx). Applying boundary conditions ψ(0) = 0 and ψ(a) = 0:
- At x = 0, ψ(0) = B = 0. Thus, ψ(x) = A sin(kx).
- At x = a, ψ(a) = A sin(ka) = 0. Since A ≠ 0, we must have sin(ka) = 0, implying ka = nπ where n = 1, 2, 3, ...
- Substituting k = nπ/a into the expression for k2: (nπ/a)2 = 2mE/ℏ2.
Solving for E, we obtain the quantized energy levels:
Since n must be an integer, the energy can only take discrete values, demonstrating that the energy of the particle is quantized.
Find the probability of finding a particle between 0.35a and 0.65a where ‘a’ is the width of the box and particle is in the first excited state.
Answer
For the first excited state, n = 2. The normalized wavefunction is ψ2(x) = √(2/a) sin(2πx/a). The probability P is given by the integral of |ψ2(x)|2 from 0.35a to 0.65a:
Using the identity sin2θ = (1 - cos 2θ)/2:
Evaluating at the limits:
The probability of finding the particle in the specified region is approximately 0.1486 or 14.86%.
Describe the Davisson and Germer’s experimental for verification of matter waves.
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Electrons are accelerated through 344 volts and are reflected from a crystal. The first reflection maximum occurs when glancing angle is 60°. Determine the spacing of the crystal. Given h = 6.62 × 10-34 Joule-sec, e = 1.6 × 10-19 C and me = 9 × 10-31 kg.
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What is a PN-junction diode? Discuss the V-I characteristics of a diode in both the biasing conditions.
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Explain advantage of Zener diode over P-N junction diode.
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Explain the Hall effect in metal? Derive the formulae to determine Hall coefficient and mobility of electrons.
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An n-type germanium sample has a donor density of 1021/m3. It is arranged in a Hall experiment having magnetic field of 0.5T and the current density is 500 A/m2. Find the Hall voltage if the sample is 3mm wide.
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What is an LED? Explain the working of LED with a neat diagram.
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Write a short note on solar cell.
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What are semiconductor diode lasers? Describe the construction and working of a semiconductor laser with energy band diagram.
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Discuss advantages of diode lasers over gas lasers.
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Draw the block diagram of an optical fibre communication system and explain the function of each block.
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Consider a fibre having a core of index 1.48, a cladding of index 1.46 and has a core diameter of 30 µm. Show that all rays making an angle less than 9.43° with the axis will propagate through the fibre.
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State and explain the basic laws of electromagnetism in their integral form.
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Distinguish between conduction current and displacement current.
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