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Question:

एक आदमी पैराशूट के साथ गिर रहा है। जब उसका पैराशूट खुलता है, उसकी चाल $50 \text{ ms}^{-1}$ है। यदि वायु प्रतिरोध (Mv²)/25 है, जहां M आदमी और पैराशूट का द्रव्यमान है, पैराशूट खुलने के बाद आदमी के चाल को समय t के फलन के रूप में प्राप्त करें। $g = 10 \text{ ms}^{-1}$ लें। (10) (नोट: छवि में g की इकाई $\text{ms}^{-1}$ लिखी है, जो संभवतः $\text{ms}^{-2}$ होनी चाहिए)

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Question:

निम्नलिखित आदि मान समस्या को हल करें :

$\frac{d^2x}{dt^2} - 3 \frac{dx}{dt} - 10x = 0, \quad x(0) = 1, \quad \dot{x}(0) = 0$

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Question:

निम्नलिखित साधारण अवकल समीकरणों को हल करें :

(i) $x dx + y dy + 4y^3(x^2 + y^2) dy = 0$

(ii) $y'' + 4y = 2 \cos x \cos 3x$

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Question:

Explain, with a diagram, the operation of a photovoltaic solar cell.

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Question:

Explain addition and condensation polymerization with an example of each.

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Question:

What are fusible alloys? Explain their use in safety sprinklers.

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Question:

The saturation magnetization of $fcc\text{ Ni}$ is $5.1 \times 10^5\text{ A/m}$ . If the lattice constant for $\text{Ni}$ is $3.52\text{ \AA}$ , calculate the net magnetic moment per $\text{Ni}$ atom in the crystal in units of Bohr magnetons.

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Question:

A metal has an fcc structure, a lattice parameter $a = 0.4\text{ nm}$ , and a valence $Z = 1$ . Calculate its Hall coefficient.

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Question:

A monovalent metal has a bcc structure and its lattice parameter is $1.5\text{ \AA}$ . Calculate its Fermi energy.

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Question:

In a p-n junction in Si, $N_d = N_a = 10^{22}\text{ m}^{-3}$ . Calculate the built in potential for Si at $300\text{ K}$ if n_i for Si at $300\text{ K} = 10^{16}\text{ m}^{-3}$ .

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Question:

Consider a superconductor with an energy gap of $1.7 \times 10^{-4}\text{ eV}$ . Find the maximum wavelength of electromagnetic radiation which will be absorbed by this superconductor.

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Question:

The values of the elastic stiffness constants for $\text{GaAs}$ are:

$C_{11}=1.18\times 10^{11}\\mathrm{N\,m^{-2}},\quad C_{44}=0.59\times 10^{11}\\mathrm{N\,m^{-2}}\quad\text{and}\quad C_{12}=0.54\times 10^{11}\\mathrm{N\,m^{-2}}.$
Given that the density of $\text{GaAs}$ is $5.32\text{ g cm}^{-3}$ , determine the bulk modulus of elasticity and the velocity of the transverse and longitudinal elastic waves in the [100] direction.

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Question:

Calculate the Debye specific heat of copper at $300\text{ K}$ , given that its Debye frequency is $4.11 \times 10^{13}\text{ rad s}^{-1}$ .

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Question:

The frequency of the longitudinal optical phonon for $\text{NaCl}$ at the centre of the first Brillouin zone is $5\text{ rad s}^{-1}$ . Calculate the interatomic force constant for this material. (The atomic weight of $\text{Na} = 23$ and $\text{Cl} = 37$ )

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Question:

The potential energy of the Neon crystal is described by the expression:

$$U(r) = -4\varepsilon \left[ \left( \frac{\rho_0}{r} \right)^6 - \left( \frac{\rho_0}{r} \right)^{12} \right]$
where $\varepsilon = 3.12 \times 10^{-3}\text{ eV}$ and $\rho_0 = 2.82\text{ \AA}$ . Calculate the lattice parameter of the Neon crystal (fcc structure).

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Question:

The potential energy of the Neon crystal is described by the expression:

$$U(r) = -4\varepsilon \left[ \left( \frac{\rho_0}{r} \right)^6 - \left( \frac{\rho_0}{r} \right)^{12} \right]$

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Question:

Show that the reciprocal lattice for an fcc lattice is a bcc lattice. If the lattice constant of the unit cell of the fcc lattice is a, determine the lattice constant for the unit cell of the reciprocal bcc lattice?

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Question:

The Bragg angle for reflection from the (110) planes in bcc iron is $22^{\circ}$ for an x-ray of wavelength $1.54\text{ \AA}$ . Find the cube edge for iron (take $n = 1$ ). What is the minimum wavelength with which the structure of this unit cell can be probed?

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Question:

Sodium metal crystallizes in the bcc structure. The metal has atomic weight 23 and density $971\text{ kg m}^{-3}$ . Calculate the cubic lattice parameter a and the shortest distance between atoms in this structure.