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*Answer can only contain numeric values

QUESTION: 1

The density of copper (Cu) is 8.90 g/m^{3} with contribution of 1 electron/atom. The plasma frequency of copper is_______x 10^{16} /s. (Given atomic weight = 63.5)(Round off to one decimal place)

Solution:

n = concentration of free electron

and for electron,

⇒

*Answer can only contain numeric values

QUESTION: 2

Assume that E vs k relationship of e^{-} in conduction band ofliypothetical tetravalent n-type semiconductor can be expressed by

E = ak^{2} + constant

The cyclotron resonance for e^{-} in a field B = 0.1 wb/m^{2} occurs at ω_{e} = 1.8 x 10^{11} rad/s

The value of a =________x 10^{-38} J. m^{2} (Round off to one decimal place)

Solution:

⇒ An e^{-} in conduction band behave as if it had an effective mass m* given by

and cyclotron resonance frequency for e^{- }is

*Answer can only contain numeric values

QUESTION: 3

The maximum wavelength of photon to break a cooper pair in Lead which has energy gap of 2.73 meV is_____________x 10^{5} nm. (Round off to three decimal places)

Solution:

*Answer can only contain numeric values

QUESTION: 4

The lattice constant of unit cell of BCC structure α - Iron is 0.288 nm. The number of atoms/mm^{2} in the plane of (1 0 0) is_____x 10^{12} atom/mm^{2}. (Answer should be an integer)

Solution:

The number of atoms in unit cell = 2 Therefore, the atomic density in (100) plane

*Answer can only contain numeric values

QUESTION: 5

For a sphere of radius x, polarised along the radius vector such that . The total charge is (Answer should be integer).

Solution:

Total charge

Thus, equation (i) implies

Total charge = -

QUESTION: 6

The metals an oppaque to light for which

Solution:

The defractive index η =

If light of frequency ω < ω_{p} incident on a metal of plasma frequency ω_{p}. than η is imaginary. This mean that such light cannot transmitted through the metal but is totally reflected from its surface.

∵ ω_{p} > ω ⇒ ε → -ve ⇒ η → imaginary

∴Thus metal is opaque to light for which ω < ω_{p}

QUESTION: 7

Optical excitation of intrinsic Germanium creates an average density of 10^{18} conduction electrons per m^{3} in the material at liquid nitrogen temperature. At this temperature electrons and holes mobilities are equal.

μ = 0.5 x 10^{4}cm^{2} /volts sec and Germanium dielectric constant is 20. The diffusion coefficient for electron is

Solution:

The diffusion coefficient D is given by Einstein relation

∵ liquid nitrogen temperature T_{D} = 77K . μ = 0.5 x 10^{-4} x 10^{4} m^{2} /V.s = 0.5 m^{2}/V.s

e = 1.6 x 10^{-19}C

k_{B} =1.38 x 10^{-23
}

QUESTION: 8

In Raman effect

Solution:

QUESTION: 9

An ac current of frequency 1 GHz is observed through Josephson junction, the applied dc voltage is

Solution:

QUESTION: 10

The polarizability 'α' of an e^{-} moving in a circular orbit of radius ‘r’ about charge +e in a field directed at light angle to plane of orbit is

Solution:

.....(i)

Dipole moment

∴

∴

*Answer can only contain numeric values

QUESTION: 11

The density of states for electron hi a metal is given by D (E)dE = 13.6x 10^{27} E^{1/2} dE and ρ = 8.5 x 10^{28} /m^{3}. The energy of Fermi level is___________eV. (Round off to three decimal places)

Solution:

*Answer can only contain numeric values

QUESTION: 12

For lead the superconductivity occurs at 7.19 k when there is zero applied magnetic field. When the magnetic field 0.074 T is applied at temperature 2.0 k superconductivity will stop. The magnetic field that should be

applied so that superconductivity will not occur at any temperature is___________x 10^{-3} T. (Answer should

be an integer).

Solution:

*Answer can only contain numeric values

QUESTION: 13

The energy of the conduction band at which the probability of the conduction electrons state will occupied by

election is 90% at T = 800K. is__________(eV). [Given: E_{F} =5.52eV]

(Round off to two decimal places)

Solution:

.......(i)

Now T = 800 K, now solving equation (i) for ΔE, we get ΔE = 5.42 eV

We get, ΔE = 5.42eV

QUESTION: 14

Calculate the relative permeability of material having magnetization of 3400 ampere/meter and flux density of 0.0045 wb/m^{2}.

Solution:

also

QUESTION: 15

A long thin uniformly magnetized needle of hard steel length 12 cm is suspended by a torsionless suspension and makes free, small angle oscillations about an axis through the center in a honzontal plane in the earth's magnetic field. The period of oscillation is four seconds. The density of magnetization of steel is

Solution:

Let μ be the magnetic moment of the steel needle. The potential energy in the earth’s magnetic field.

T = 4s

B = 5 x 10 ^{-5} wm^{-2}

M → Magnetization

Using (i), (ii) and (iii)

QUESTION: 16

The energy of interaction of two atoms at a distane 'r' apait can be written as

where, a, b are constants

If two atoms are pulled apart show that they will separete most easily when

Solution:

The particles will separate most easily when force F is minimum. Now, F to be minimum,

QUESTION: 17

Consider a crystal containing a paramagnetic impurity whose energy level are in a given magnetic field. The specific heat of the crystal at high temperature will vary with

Solution:

The contribution of impurity to the partition function of the crystal is z =

At high temperature

Thus,

QUESTION: 18

A rough sketch of the absorbtion co-efficient for the EM radiation for a non magnetic pure solid substance. The solid absorb light in infrared (0.15 eV) and then does not absorb until the photon energy is 2.3 eV. The minimum number of atoms per unit cell in the crystal should be

Solution:

There are minimum more than 2 atoms per unit cell otherwise the optical branch would have been absent and there would be no absorbtion peak at 0.15 eV.

QUESTION: 19

X-rays are reflected from a simple cubic crystal by Bragg reflection. If the density of the crystal is measured with r.m.s. error of 3 parts in 10^{4} and if the angle made by the incident and reflected ray make with the crystal plane is 6° and is measured with an r.m.s. error 3.4 minutes of arc then what is the error in the determination of wavelength.

Solution:

For simple cubic crystal n = 1.

For first order reflection 2d sin θ = λ

∵

QUESTION: 20

The basis vectors of a lattice is given by

The volume of the reciprocal lattice are given by

Solution:

Volume ot unit cell in direct lattice.

Therefore, basic vectors of reciprocal lattice are given by

Therefore, volume of unit cell in reciprocal Lattice.

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