GATE PH exam:gate PYQs & Answers — Page 25

Questions 241–250 of 650. Imported answers require independent review unless marked reviewed.

In the first Brillouin zone of a rectangular lattice (lattice constants

Å and

Å), three incoming phonons with the same wave vector ⟨1.2 Å

, 0.6 Å

⟩ interact to give one phonon. Which one of the following is the CORRECT wave vector of the resulting phonon?

Your answerChoose one option.

⟨2.56 Å

, 0.23 Å

⟩

⟨3.60 Å

, 1.80 Å

⟩

⟨0.48 Å

, 0.23 Å

⟩

⟨3.60 Å

, −0.80 Å

⟩

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For a covalently bonded solid consisting of ions of mass

, the binding potential can be assumed to be given by

where

and

are positive constants. What is the Einstein frequency of the solid in Hz?

Your answerChoose one option.

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In a hadronic interaction,

s are produced with different momenta, and they immediately decay into two photons with an opening angle

between them. Assuming that all these decays occur in one plane, which one of the following figures depicts the behavior of

as a function of the

momentum

Your answerChoose one option.

Diagram for Physics question 48 (figure 2)

Diagram for Physics question 48 (figure 3)

Diagram for Physics question 48 (figure 4)

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A particle has wavefunction

where

is a normalization constant and

is a positive constant. In this state, which one of the following options represents the eigenvalues of

and

respectively?

Some values of

are:

Your answerChoose one option.

and

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The wavefunction of a particle in one dimension is given by

Here

and

are positive constants. If

is the corresponding momentum space wavefunction, which one of the following plots best represents

Your answerChoose one option.

Diagram for Physics question 50 (figure 2)

Diagram for Physics question 50 (figure 3)

Diagram for Physics question 50 (figure 4)

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Consider a particle in a two dimensional infinite square well potential of side

, with

and

. The wavefunction of the particle is zero only along the line

, apart from the boundaries of the well. If the energy of the particle in this state is

, what is the energy of the ground state?

Your answerChoose one option.

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Consider two non-identical spin

particles labelled 1 and 2 in the spin product state

. The Hamiltonian of the system is

where

and

are the spin operators of particles 1 and 2, respectively, and

is a constant with appropriate dimensions. What is the expectation value of

in the above state?

Your answerChoose one option.

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A spin

particle is in a spin up state along the

-axis (with unit vector

) and is denoted as

. What is the probability of finding the particle to be in a spin up state along the direction

, which lies in the

-plane and makes an angle

with respect to the positive

-axis, if such a measurement is made?

Your answerChoose one option.

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Different spectral lines of the Balmer series (transitions

, with

being the principal quantum number) fall one at a time on a Young’s double slit apparatus. The separation between the slits is

and the screen is placed at a constant distance from the slits. What factor should

be multiplied by to maintain a constant fringe width for various lines, as

takes different allowed values?

Your answerChoose one option.

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Under parity and time reversal transformations, which of the following statements is(are) TRUE about the electric dipole moment

and the magnetic dipole moment

Your answerSelect all correct options. You can choose more than one.

is odd under parity and

is odd under time reversal

is odd under parity and

is even under time reversal

is even under parity and

is odd under time reversal

is even under parity and

is even under time reversal

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GATE PH exam:gate PYQs

Question 46

Question 47

Question 48

Question 49

Question 50

Question 51

Question 52

Question 53

Question 54

Question 55