Back to Subject

Unit 4: Quantum Mechanics - Practice Quiz

PHY109 — Engineering Physics 60 Questions
0 Correct 0 Wrong 60 Left
0/60

1 Quantum mechanics is mainly needed to describe the behavior of which systems?

Need for quantum mechanics Easy
A. Microscopic particles
B. Large buildings
C. Planetary orbits
D. Moving vehicles

2 Which observation could not be explained correctly by classical physics?

Need for quantum mechanics Easy
A. Reflection by a mirror
B. Photoelectric effect
C. Motion of a pendulum
D. Expansion of a solid

3 An ideal black body is an object that absorbs what fraction of the radiation incident on it?

Black-body radiation: spectral distribution Easy
A. Half of it
B. None of it
C. All of it
D. One-fourth of it

4 According to Wien's displacement law, what happens to the peak wavelength of black-body radiation as temperature increases?

Black-body radiation: spectral distribution Easy
A. It becomes shorter
B. It becomes longer
C. It becomes infinite
D. It remains constant

5 What are the electrons emitted from a metal surface due to incident light called?

Photoelectric effect Easy
A. Free neutrons
B. Alpha particles
C. Positive ions
D. Photoelectrons

6 Which equation represents Einstein's photoelectric equation?

Photoelectric effect Easy
A.
B.
C.
D.

7 According to de Broglie, which entities exhibit wave-like behavior?

Concept of de Broglie matter waves Easy
A. Only stationary objects
B. All moving particles
C. Only charged particles
D. Only visible photons

8 Which experiment demonstrated the wave nature of electrons?

Concept of de Broglie matter waves Easy
A. Millikan oil-drop experiment
B. Davisson-Germer experiment
C. Rutherford scattering experiment
D. Michelson-Morley experiment

9 What is the de Broglie wavelength of a particle having momentum ?

Wavelength of matter waves in different forms Easy
A.
B.
C.
D.

10 For a non-relativistic particle of mass moving with speed , which expression gives its de Broglie wavelength?

Wavelength of matter waves in different forms Easy
A.
B.
C.
D.

11 The velocity with which a point of constant phase travels is called what?

Concept of phase velocity and group velocity (qualitative) Easy
A. Phase velocity
B. Group velocity
C. Drift velocity
D. Escape velocity

12 Which velocity is associated with the propagation of a wave packet?

Concept of phase velocity and group velocity (qualitative) Easy
A. Group velocity
B. Terminal velocity
C. Phase velocity
D. Angular velocity

13 Which pair of physical quantities is related by Heisenberg's uncertainty principle?

Heisenberg uncertainty principle Easy
A. Pressure and volume
B. Speed and density
C. Mass and charge
D. Position and momentum

14 Which mathematical relation expresses the uncertainty principle for position and momentum?

Heisenberg uncertainty principle Easy
A.
B.
C.
D.

15 What does represent in quantum mechanics?

Wave function and its significance Easy
A. Wave frequency
B. Total energy
C. Particle momentum
D. Probability density

16 Which property must a physically acceptable wave function possess?

Wave function and its significance Easy
A. It must be discontinuous
B. It must be finite
C. It must be multivalued
D. It must be infinite

17 Which symbol commonly represents the Hamiltonian operator in the Schrödinger equation?

Schrodinger time-dependent and time-independent equations Easy
A.
B.
C.
D.

18 The time-independent Schrödinger equation is commonly written in which form?

Schrodinger time-dependent and time-independent equations Easy
A.
B.
C.
D.

19 For a particle in a one-dimensional infinite box, what is the wave function at the walls?

Particle in a box Easy
A. Constant
B. One
C. Zero
D. Infinite

20 Which quantum numbers are allowed for a particle in a one-dimensional infinite box?

Particle in a box Easy
A.
B.
C.
D.

21 Which experimental observation most directly contradicts the classical prediction that a black body emits unlimited energy at short wavelengths?

Need for quantum mechanics Medium
A. The refraction of light through a prism
B. The finite peak in the black-body spectrum
C. The reflection of light from a mirror
D. The interference of two coherent waves

22 A star behaves approximately as a black body at . Using Wien's law, , estimate its peak wavelength.

Black-body radiation: spectral distribution Medium
A.
B.
C.
D.

23 The absolute temperature of a black body is doubled. How does the wavelength at which its spectral intensity is maximum change?

Black-body radiation: spectral distribution Medium
A. It becomes twice as large
B. It remains exactly unchanged
C. It becomes four times larger
D. It becomes half as large

24 Light of wavelength falls on a metal with work function . Using , what is the stopping potential?

Photoelectric effect Medium
A.
B.
C.
D.

25 The intensity of monochromatic light above the threshold frequency is doubled while its frequency remains fixed. What happens in an ideal photoelectric experiment?

Photoelectric effect Medium
A. Stopping potential halves while maximum kinetic energy is unchanged
B. Photocurrent doubles while maximum kinetic energy is unchanged
C. Both photocurrent and maximum kinetic energy become doubled
D. Maximum kinetic energy doubles while photocurrent is unchanged

26 A metal has a work function of . Using , estimate its threshold frequency.

Photoelectric effect Medium
A.
B.
C.
D.

27 An electron and a neutron have equal magnitudes of momentum. How do their de Broglie wavelengths compare?

Concept of de Broglie matter waves Medium
A. Their wavelength ratio equals their mass ratio
B. The electron wavelength is larger
C. The neutron wavelength is larger
D. Their wavelengths are equal

28 An electron is accelerated from rest through a potential difference of . Using , find its de Broglie wavelength.

Wavelength of matter waves in different forms Medium
A.
B.
C.
D.

29 A nonrelativistic electron and proton have the same kinetic energy. Approximately what is the ratio ?

Wavelength of matter waves in different forms Medium
A.
B.
C.
D.

30 A proton and an alpha particle are accelerated from rest through the same potential difference. Taking and , what is ?

Wavelength of matter waves in different forms Medium
A.
B.
C.
D.

31 For a relativistic matter-wave packet representing a freely moving particle of speed , which statement is correct?

Concept of phase velocity and group velocity (qualitative) Medium
A. for every particle
B. and
C. for every particle
D. and

32 In a wave packet, what do the group velocity and phase velocity respectively describe?

Concept of phase velocity and group velocity (qualitative) Medium
A. Envelope motion and individual phase-front motion
B. Phase-front motion and envelope motion
C. Wave amplitude and particle acceleration
D. Particle acceleration and wave amplitude

33 An electron is localized with position uncertainty . Using , what is the minimum uncertainty in its velocity? Take and .

Heisenberg uncertainty principle Medium
A.
B.
C.
D.

34 An excited state has a lifetime uncertainty of . Using , estimate its minimum energy uncertainty. Take .

Heisenberg uncertainty principle Medium
A.
B.
C.
D.

35 Inside a one-dimensional box of length , a wave function is . If it is normalized, what is the positive value of ?

Wave function and its significance Medium
A.
B.
C.
D.

36 Two normalized wave functions are related by , where is a constant real phase. Which statement is correct?

Wave function and its significance Medium
A. They predict identical probability densities
B. They predict different position probabilities
C. Only represents a physical state
D. Only satisfies normalization

37 For a time-independent potential, a separated solution has the form . Which equation must satisfy?

Schrodinger time-dependent and time-independent equations Medium
A.
B.
C.
D.

38 A system with a time-independent potential is in a single energy eigenstate. How does its probability density change with time?

Schrodinger time-dependent and time-independent equations Medium
A. It increases linearly with time
B. It remains independent of time
C. It oscillates with angular frequency
D. It decreases exponentially with time

39 For a particle in a one-dimensional infinite box, . What is the ratio ?

Particle in a box Medium
A.
B.
C.
D.

40 An electron in a infinite box drops from to . If and , what is the emitted photon's wavelength?

Particle in a box Medium
A.
B.
C.
D.

41 The Rayleigh–Jeans law predicts . If it is integrated only over wavelengths , how does the predicted total energy density behave as , and what experimental fact contradicts it?

Need for quantum mechanics Hard
A. It approaches a constant, whereas the measured total energy density diverges.
B. It grows logarithmically, whereas the measured spectrum is temperature-independent.
C. It grows as , whereas the measured peak wavelength is finite.
D. It grows as , whereas the measured total energy density is finite.

42 Planck's mean energy per oscillator is . Which expansion correctly recovers the classical limit while showing the leading quantum corrections for ?

Need for quantum mechanics Hard
A.
B.
C.
D.

43 For Planck's wavelength spectral radiance , compare with . What is their ratio?

Black-body radiation: spectral distribution Hard
A.
B.
C.
D.

44 The maxima of and satisfy and , respectively. For the same temperature, what is ?

Black-body radiation: spectral distribution Hard
A.
B.
C.
D.

45 A metal has stopping potential at frequency and at frequency . Neglect contact potentials. What are and the work function ?

Photoelectric effect Hard
A. and
B. and
C. and
D. and

46 A metal has threshold wavelength . Light of wavelength ejects nonrelativistic electrons. What is the de Broglie wavelength of the fastest electron in terms of the work function ?

Photoelectric effect Hard
A.
B.
C.
D.

47 For a particle moving around a closed orbit, which condition follows from requiring its de Broglie wave to be single-valued after one complete traversal?

Concept of de Broglie matter waves Hard
A.
B.
C.
D.

48 A nonrelativistic electron and neutron have the same de Broglie wavelength. Ignoring interactions, which pair of relations is correct?

Concept of de Broglie matter waves Hard
A. and
B. and
C. and
D. and

49 An electron and a proton, initially at rest, are accelerated through the same nonrelativistic potential difference. What is ?

Wavelength of matter waves in different forms Hard
A.
B.
C.
D.

50 An electron is accelerated from rest through . Using , what is the ratio of its relativistic de Broglie wavelength to the nonrelativistic estimate?

Wavelength of matter waves in different forms Hard
A.
B.
C.
D.

51 For a narrow wave packet representing a free nonrelativistic particle, and . How are its phase velocity , group velocity , and particle speed related?

Concept of phase velocity and group velocity (qualitative) Hard
A. and
B. and
C. and
D. and

52 For a relativistic massive-particle wave packet obeying , which statement is correct?

Concept of phase velocity and group velocity (qualitative) Hard
A. , and both velocities equal the classical particle speed.
B. , and the superluminal does not transmit information.
C. , and both velocities may exceed the speed of light.
D. , and the superluminal does not transmit information.

53 An electron is prepared with , , and minimum position–momentum uncertainty. What is its minimum mean kinetic energy?

Heisenberg uncertainty principle Hard
A.
B.
C.
D.

54 A particle is known to lie within an interval of width . Using only and Heisenberg's relation, the kinetic-energy lower bound is . For an infinite square well of the same width, what is ?

Heisenberg uncertainty principle Hard
A.
B.
C.
D.

55 Inside , a wave function is and is zero outside. Which pair gives its normalization constant and position variance?

Wave function and its significance Hard
A. and
B. and
C. and
D. and

56 Let and be real energy eigenfunctions of opposite parity, with and energies . If , what is ?

Wave function and its significance Hard
A.
B.
C.
D.

57 For a time-independent Hamiltonian, let and be distinct normalized energy eigenstates. Which statement about is correct?

Schrodinger time-dependent and time-independent equations Hard
A. It solves the time-dependent equation, but its probability density is generally time-dependent.
B. It fails to solve either equation because two energies are present.
C. It is stationary because each component has a unit-modulus phase factor.
D. It solves the time-independent equation with energy .

58 A constant is added everywhere to a time-independent potential. If was a solution before the shift, which transformed solution and physical consequence are correct?

Schrodinger time-dependent and time-independent equations Hard
A. ; all momentum eigenvalues shift by while energies remain unchanged.
B. ; all energy eigenvalues shift by while probabilities remain unchanged.
C. ; all energy eigenvalues shift by while currents reverse.
D. ; all energy eigenvalues scale by while probabilities remain unchanged.

59 A particle in an infinite well has normalized state . What is its expectation value of energy?

Particle in a box Hard
A.
B.
C.
D.

60 For the normalized state in an infinite well , what is the probability that an energy measurement gives the ground-state energy?

Particle in a box Hard
A.
B.
C.
D.
Previous MCQ
Unit 3
Next MCQ
Unit 5