National Testing Agency
Question Paper Name : Introduction to Quantum Physics
Subject Name : Introduction to Quantum Physics
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Creation Date : 2020-09-15 13:26:32
Duration : 180
Total Marks : 90
Display Marks: Yes
Share Answer Key With Delivery Engine : Yes
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Actual Answer Key : Yes
Introduction to Quantum Physics and its Application
Group Number : 1
Group Id : 89951413
Group Maximum Duration : 0
Group Minimum Duration : 120
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Show Attended Group? : No
Edit Attended Group? : No
Break time: 0
Group Marks : 90
Is this Group for Examiner? : No
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Introduction to Quantum Physics and its Application
Section Id : 89951413
Section Number : 1
Section type : Online
Mandatory or Optional : Mandatory
Number of Questions : 15
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Number of Questions to be attempted : 15
Section Marks : 90
Display Number Panel : Yes
Group All Questions : Yes
Mark As Answered Required? : Yes
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Sub-Section Number : 1
Sub-Section Id : 89951422
Question Shuffling Allowed : Yes
Question Number : 1 Question Id : 8995141011 Question Type : MCQ Option Shuffling : No Display Question Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 6 Wrong Marks : 0
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The energy density u of radiation in a blackbody, in thermal equilibrium at temperature T, is also a function of the frequency of radiation v. The function u(v, T)? 0 for both v?0 and v?8. It attains its maximum value for some Vmax. The approximate value of Vmax is (k and h are Boltzmann and Planck constants respectively)
(A) kT/h
(B) 2kT/h
(C) 3kT/h
(D) 4kT/h
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Options:
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Question Number : 2 Question Id: 8995141012 Question Type: MCQ Option Shuffling : No Display Question
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 6 Wrong Marks : 0
A light of frequency v is incident on a metal and a photocurrent was emitted. This photocurrent is stopped when a potential Vs (stopping potential) is applied to the metal. An experiment is performed with different values of v and the corresponding Vs values were measured. The relation between Vs and v is
(A) Vs = av
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(B) Vs = av - b
(C) Vs = av²
(D) Vs = av² - b
In the above equations, a and b are constants of appropriate dimensions.
Options:
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Question Number : 3 Question Id : 8995141013 Question Type : MCQ Option Shuffling : No Display Question
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Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 6 Wrong Marks : 0
Consider a new kind of atom where the electron is in a circular orbit about a proton. If the binding energy of the n-th orbit is given by En = -Eo/n, where Eo is a constant, the angular momentum of this orbit is given by
(A) n²h
(B) nh
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(C) n1/2h
(D) nh
Options:
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Question Number : 4 Question Id : 8995141014 Question Type : MCQ Option Shuffling : No Display Question
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 6 Wrong Marks : 0
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A particle is in a state described by the wavefunction
?(x) = N / (x²+a²),
where N is the normalization constant and a is a constant with dimension of length. The uncertainty in the position coordinate of the particle is
(A) a/v2
(B) a
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(C) av2
(D) 2a
Options:
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Question Number : 5 Question Id : 8995141015 Question Type : MCQ Option Shuffling : No Display Question
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 6 Wrong Marks : 0
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A particle of mass m is confined to a 1-dimensional region [0, a], normalized wave function is
?(x) = v(8/5a) [1+cos(px/a)]sin(px/a)
The average energy of the particle is
(A) (5p²h²)/(4ma²)
(B) (6p²h²)/(5ma²)
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(C) (4p²h²)/(5ma²)
(D) (5p²h²)/(6ma²)
Options:
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Question Number : 6 Question Id : 8995141016 Question Type : MCQ Option Shuffling : No Display Question
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 6 Wrong Marks : 0
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Consider a stream of particles of mass m, each moving in the positive x-direction with kinetic energy E towards a potential jump located at x = 0. The potential is zero for x = 0 and 3E/4 for x > 0. The fraction of particles will be reflected back at x = 0 will be
(A) 1/9
(B) 1/6
(C) 1/4
(D) 1/3
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Options:
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Question Number : 7 Question Id : 8995141017 Question Type : MCQ Option Shuffling : No Display Question
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 6 Wrong Marks : 0
An operator Â, representing observable A, has two normalized eigenstates ?1 and ?2, with eigenvalues a1 and a2, respectively. Operator B, representing observable B, has two normalized eigenstates f1 and f2, with eigenvalues b1 and b2, respectively. The eigenstates are related by
?1 = (3f1+4f2)/v5, ?2=(4f1-3f2)/v5
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After preparing the system in a general state, observable B is first measured, and the value b1 is obtained. If A is measured immediately afterwards, the possible results for the probabilities of finding eigenvalues a1 and a2 are
(A) 9/25 and 16/25
(B) 16/25 and 9/25
(C) 3/5 and 4/5
(D) 4/5 and 3/5
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Options:
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Question Number : 8 Question Id : 8995141018 Question Type : MCQ Option Shuffling : No Display Question
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 6 Wrong Marks : 0
Consider a particle of mass m moving in a 1-dimensional potential well of width a:
V(x) = 8, x < 0
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= 0, 0 = x = a
= Vo, x > a
The bound state energies (E<Vo) of the particle in such a potential well are given by
(A) tan(av(2mE)/h) = -v(Vo-E)/E
(B) tan(av(2mE)/h) = v(E/(Vo-E))
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(C) tan(av(2mE)/h) = v(Vo-E)/vE
(D) tan(av(2mE)/h) = -v(E/(Vo-E))
Options:
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Question Number : 9 Question Id : 8995141019 Question Type : MCQ Option Shuffling : No Display Question
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 6 Wrong Marks : 0
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Sodium is a metal with electrical conductivity 2.17 × 107 O-1m-1. If sodium is kept in a field of 200 Vm-1, the drift velocity (in m/sec) of the electron will be (assume that only one conduction electron is available for each sodium atom). (Given, density of Sodium = 970 Kg m-3, atomic mass of Sodium = 23 amu, charge of electron=1.6 × 10-19 Coulomb, Avogadro's number = 6.0 × 1023)
(A) 1.1
(B) 9.1
(C) 50.1
(D) 120.1
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Options:
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Question Number : 10 Question Id : 8995141020 Question Type : MCQ Option Shuffling : No Display Question
Question Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 6 Wrong Marks : 0
The density of copper is 8.94 gm cm-3 and its atomic weight is 63.5 per molecule, the effective mass of electron being 1.01. Assume that each atom gives one electron, calculate the average energy <E> of the free electrons at 0°K. The temperature (in Kelvin) required for the average kinetic energy of gas molecules to posses this value of < E > is
(A) 3.22 × 104
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(B) 9.22 × 104
(C) 3.22 × 103
(D) 9.22 × 103
Options:
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Question Number : 11 Question Id : 8995141021 Question Type : MCQ Option Shuffling : No Display Question
Question Mandatory : No Single Line Question Option : No Option Orientation : Vertical
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Correct Marks : 6 Wrong Marks : 0
A 3D confinement potential V(x, y, z) is defined as follows:
V(x, y, z) = V(x)+V(y)+V(z)
where, for 0 < z < L (for all x and y)
V(x,y)=V(x)+V(y)= ½mw²(x²+y²) and V(z)=0
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and for z=0 and z=L (for all x and y)
V(x, y, z) = 8
Consider L = pv(h/(10mw)). The degeneracy of the state with energy E = 19hw is
(A) 19
(B) 14
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(C) 13
(D) 4
Options:
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Question Number : 12 Question Id : 8995141022 Question Type : MCQ Option Shuffling : No Display Question
Question Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 6 Wrong Marks : 0
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Assume the energy of an electron in a band of 1-dimensional solid is given by
E(k) = E0 sin²(ka/2)
The effective mass of the electron, when ka = p/3, is
(A) h²/(a²E0)
(B) 2h²/(a²E0)
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(C) 3h²/(a²E0)
(D) 4h²/(a²E0)
Options:
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Question Number : 13 Question Id : 8995141023 Question Type : MCQ Option Shuffling : No Display Question
Question Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 6 Wrong Marks : 0
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For a particle moving in 1-dimension, the phase space is a plane with position plotted along horizontal axis and velocity v plotted along vertical axis. Some possible phase space figures are shown below. Which one of these figures does NOT represent the motion of a free electron?
(A) (i)
(B) (ii)
(C) (iii)
(D) (iv)
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Options:
Question Number : 14 Question Id : 8995141024 Question Type : MCQ Option Shuffling : No Display Question
Question Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 6 Wrong Marks : 0
A one dimensional, finite potential barrier has the form
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V(x) = 0 for -8<x<0
= Vo for 0<x<L
=0 for L<x<8
where Vo is a positive constant. A beam of particles with kinetic energy 0< is incident on the barrier from x = -8. The probability of a particle tunneling through the barrier varies with the width of the well (L) as
(A) 1/L
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(B) 1/L²
(C) exp(-aL), where a is a constant of appropriate dimension
(D) exp(-ßL²), where ß is a constant of appropriate dimension
Options:
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