GATE PH format:nat PYQs & Answers — Page 5

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Questions 41–50 of 182. Imported answers require independent review unless marked reviewed.

Topic practice 182 questionsPage 5 of 19

An electron in the Coulomb field of a proton is in the following state of coherent superposition of orthonormal states

Let

, and

represent the first three energy levels of the system. A sequence of measurements is done on the same system at different times. Energy is measured first at time

and the outcome is

. Then total angular momentum is measured at time

and finally energy is measured again at

. The probability of finding the system in a state with energy

after the final measurement is

. The value of

is _____ (in integer).

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According to the nuclear shell model, the absolute value of the difference in magnetic moments of

and

, in the units of nuclear magneton (

) is

. The magnitude of

is _____ (in integer).

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In the vector model of angular momentum applied to atoms, what is the minimum angle in degrees (in integer) made by the orbital angular momentum vector and the positive

axis for a

electron?

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For a transistor amplifier, the frequency response is such that the mid band voltage gain is 200. The cutoff frequencies are 20 Hz and 20 kHz. What is the ratio (rounded off to two decimal places) of the voltage gain at 10 Hz to that at 100 kHz?

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An electric field as a function of radial coordinate

has the form

, where

is a constant. Assume that dimensions are appropriately taken care of. The electric flux through a sphere of radius

, centered at the origin, is

. What is the value of

(rounded off to two decimal places)?

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Two independent electrostatic configurations are shown in the figure. Configuration

consists of an isolated point charge

, and configuration

consists of another identical charge surrounded by a thick conducting shell of inner radius

and outer radius

, with the charge at the center of the shell.

and

, where

and

are the magnitudes of the electric fields for configurations

and

respectively,

is the permittivity of vacuum, and the volume integrations are carried out over all space. If

, what is the value of the integer

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In pion nucleon scattering, the pion and nucleon can combine to form a short lived bound state called the

particle

. The masses of the pion, nucleon and the

particle are 140 MeV/

, 938 MeV/

and 1230 MeV/

, respectively. In the lab frame, where the nucleon is at rest, what is the minimum energy (in MeV/

, rounded off to one decimal place) of the pion to produce the

particle?

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Consider an electromagnetic wave propagating in the

-direction in vacuum, with the magnetic field given by

. If

, the average power passing through a circle of radius 1.0 m placed in the

plane is

(in Watts). Using

, what is the value of

(rounded off to one decimal place)?

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-particle is emitted from the decay of Americium (Am) at rest, i.e.,

. The rest masses of

and

are 224.544 GeV/

, 220.811 GeV/

and 3.728 GeV/

respectively. What is the kinetic energy (in MeV/

, rounded off to two decimal places) of the

-particle?

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Consider 6 identical, non-interacting, spin

atoms arranged on a crystal lattice at absolute temperature

. The

-component of the magnetic moment of each of these atoms can be

. If

and

are the probabilities of the net magnetic moment of the solid being

and

respectively, what is the value of

(in integer)?

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GATE PH format:nat PYQs

Question 64

Question 65

Question 33

Question 34

Question 35

Question 59

Question 60

Question 61

Question 62

Question 63