Solve your IGNOU Doubts

Question:

b) State Moseley’s law. Using this law, obtain the frequency of an X-ray line when L to K transition takes place in a silver atom. Take $\sigma =3.$

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Question:

A semiconductor has the following parameters at temperature T = 300 K:

$\mathrm{E_{g}=1.40\ e V.\;\ m_{e}^{*}=0.1\ m_{e}\,\cdot m_{h}^{*}=0.5\ m_{e}.}$

Calculate the energy of the intrinsic Fermi level and the intrinsic carrier concentration.

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Question:

A 2-D square lattice has a side of 1.5 Å. Calculate the momentum and energy of the electron whose wave terminates at the boundary of the first Brillouin zone.

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Question:

A divalent bcc solid has a lattice constant of 4.5 Å. Calculate its Fermi energy.

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Question:

a) Calculate the mean kinetic energy and potential energy of the 1-dimensional oscillator in the ground state having angular velocity $\omega .$

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Question:

A divalent bcc solid has a lattice constant of 4.5 Å. Calculate its Fermi energy.

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Question:

Prove that in a crystal undergoing deformation, the deformed crystal axes are not mutually perpendicular.

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Question:

e) The wave function of a particle moving in the x-direction is given by:

$\Psi (x)=\left\{\begin{matrix} Nx(l-x) ,& 0<x<L\\0\,\,\,\,\,,elsewhere & \end{matrix}\right.$

Calculate the normalization constant.

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Question:

The Debye temperatures of NaCl and KCl are 330 K and 220 K respectively. If the heat capacity of KCl at 5 K is $3.8\times10^{-2}J\,mol^{-1}K^{1}$ , calculate the heat capacity of NaCl at 15 K.

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Question:

d) Calculate the commutator $\left [ p,e^{ik0x} \right ]$ where the function $e^{ik0x}$ may be expanded as: $e^{ik0x}=\sum _{n=0}^{\infty }\frac{(ik_0x)^n}{n!}$

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Question:

The Young’s modulus of a linear mono-atomic chain of atoms of mass $10.6\times10^{-26}kg\,is\,2.0\times10^{11}Nm^{-2}.$ . If the inter-atomic separation is $2.8\,\AA$ , calculate the force constant K and the maximum frequency of the atoms.

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Question:

c) A particle of mass m and zero energy has a wave function $\Psi (x)=N\,xe\frac{-x^2}{16},$ where N is a constant. Determine the potential energy $V(x)$ for the particle

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Question:

The binding energy of CsCl is 150 kcal mol^-1 If the Madelung constant for CsCl is 1.763 and the repulsive exponent $n=10.6,$ calculate the equilibrium interatomic distance $r_e.$ (Take $\varepsilon_0=8.86\times10^{-12}$ Farad $m^{-1}$ .)

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Question:

b) Calculate the deBroglie wavelength of a $^{87}Rb$ atom that has been laser cooled to $120\,\pi K.$ (Assume that the kinetic energy is $\frac{3}{2}k_BT).$

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Question:

$\vec{a}_1=a \left ( \frac{\sqrt{3}}{2}\hat{i}+\frac{1}{2}\hat{j} \right );\vec{a}_2=a\left ( -\frac{\sqrt{3}}{2}\hat{i}+\frac{1}{2}\hat{j} \right )$ and $\vec{a}_3=c\hat{k}$

Obtain the volume of the primitive unit cell and the reciprocal lattice vectors.

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Question:

a) Using Heisenberg’s uncertainty principle, estimate the energy and radius of the ground state of a hydrogen-like atom made of a proton and a muon. Assume that the

proton and the muon are bound by the Coulomb potentia $V(r)=\frac{e^2}{4\pi \varepsilon0r }.$ The mass of the muon is $106\,MeV/c^{2}.$

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Question:

e) A star emits light with wavelength 120 nm. An observer on earth measures the wavelength of the light received from the star to be 600 nm. Calculate the speed with which the star is moving

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Question:

d) Missiles are fired towards the earth from a spacecraft. The missiles are moving with a speed of 0.8c with respect to the spacecraft. If the spacecraft itself has a speed of 0.3c with respect to Earth, how fast are the missiles observed to travel with respect to Earth

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Question:

c) The rest energy of a proton is 938 MeV. If its kinetic energy is also 938MeV, calculate its momentum and speed.

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Question:

b) Supersonic jets are able to achieve maximum speeds of up to $3.0\times 10^{-1}c.$ Calculate the percentage contraction in the length of a jet plane travelling at this speed.