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Unit 4 - Practice Quiz

PHY109

1 Which phenomenon could not be explained by classical mechanics, leading to the development of quantum mechanics?

A. Interference of light
B. Diffraction of light
C. Black body radiation spectrum
D. Polarization of light

2 According to Planck's quantum theory, energy is emitted or absorbed in discrete packets called quanta. What is the energy of a single quantum of frequency ?

A.
B.
C.
D.

3 In the context of Black Body radiation, Wien's displacement law states that the product of wavelength corresponding to maximum intensity () and absolute temperature () is:

A. Zero
B. Infinity
C. A constant
D. Variable depending on the material

4 Which law of black body radiation successfully explains the energy distribution at longer wavelengths but fails at shorter wavelengths?

A. Wien's Law
B. Rayleigh-Jeans Law
C. Planck's Law
D. Stefan's Law

5 In the photoelectric effect, the minimum frequency of incident radiation required to eject an electron from a metal surface is called:

A. Stopping frequency
B. Threshold frequency
C. Kinetic frequency
D. Resonant frequency

6 Einstein's photoelectric equation is given by which of the following? (Where is max kinetic energy, is incident energy, and is work function)

A.
B.
C.
D.

7 Who proposed the concept of matter waves, stating that moving particles exhibit wave-like properties?

A. Werner Heisenberg
B. Erwin Schrodinger
C. Louis de Broglie
D. Max Planck

8 The de Broglie wavelength of a particle with momentum is given by:

A.
B.
C.
D.

9 If the kinetic energy of a non-relativistic particle of mass is doubled, how does its de Broglie wavelength change?

A. It becomes times the original.
B. It becomes times the original.
C. It becomes half the original.
D. It remains unchanged.

10 What is the de Broglie wavelength of an electron accelerated through a potential difference of volts? (Approximate formula)

A. nm
B.
C.
D.

11 For thermal neutrons at temperature , the de Broglie wavelength is proportional to:

A.
B.
C.
D.

12 The velocity with which the phase of a wave travels is known as:

A. Group velocity
B. Phase velocity
C. Particle velocity
D. Drift velocity

13 Group velocity () is defined mathematically as:

A.
B.
C.
D.

14 For a non-relativistic material particle, the group velocity of the matter wave is equal to:

A. The phase velocity
B. The velocity of light
C. The particle velocity
D. Zero

15 In a non-dispersive medium, the relationship between phase velocity () and group velocity () is:

A.
B.
C.
D.

16 The Heisenberg Uncertainty Principle states that it is impossible to simultaneously determine with arbitrary precision which pair of variables?

A. Energy and Velocity
B. Position and Momentum
C. Charge and Mass
D. Position and Time

17 The mathematical form of the Heisenberg Uncertainty Principle for position () and momentum () is:

A.
B.
C.
D.

18 Using the Uncertainty Principle, which of the following can be explained?

A. Photoelectric effect
B. Non-existence of electrons in the nucleus
C. Black body radiation
D. Compton effect

19 The uncertainty principle relating energy () and time () is given by:

A.
B.
C.
D.

20 Why is the Heisenberg uncertainty principle not observed in macroscopic objects?

A. Planck's constant is too large.
B. Planck's constant is extremely small relative to macroscopic scales.
C. Macroscopic objects do not move.
D. Macroscopic objects have no wave nature.

21 A wave function in quantum mechanics represents:

A. The exact path of a particle
B. The probability amplitude of a particle
C. The energy density of a particle
D. The charge density of a particle

22 According to Max Born's interpretation, the quantity represents:

A. Electric charge
B. Momentum density
C. Position probability density
D. Energy density

23 For a wave function to be physically acceptable, it must satisfy which of the following conditions?

A. It must be discontinuous.
B. It must be infinite at some points.
C. It must be single-valued and continuous.
D. It must have multiple values at a single point.

24 The condition is known as the:

A. Orthogonality condition
B. Normalization condition
C. Uncertainty condition
D. Continuity condition

25 The Schrodinger Time-Independent Wave Equation for a particle of mass moving in potential is:

A.
B.
C.
D.

26 In the Schrodinger wave equation, the operator for momentum is:

A.
B.
C.
D.

27 The Hamiltonian operator in Schrodinger's equation corresponds to which physical quantity?

A. Momentum
B. Total Energy
C. Kinetic Energy
D. Potential Energy

28 For a particle in a 1D rigid box of length , the potential energy inside the box () is:

A.
B. $1$
C. $0$
D.

29 For a particle in a 1D rigid box of length , the potential energy outside the box is:

A. $0$
B. Finite constant
C.
D. Negative

30 The allowed energy levels for a particle of mass in a 1D box of width are given by:

A.
B.
C.
D.

31 In the particle in a box problem, the integer is called the:

A. Refractive index
B. Quantum number
C. Phase constant
D. Decay constant

32 What is the lowest possible energy (Zero Point Energy) for a particle in a 1D box?

A.
B.
C.
D.

33 The wave function for a particle in a 1D box of length is proportional to:

A.
B.
C.
D.

34 For a particle in a box, as the size of the box increases, the spacing between energy levels:

A. Increases
B. Decreases
C. Remains constant
D. Becomes zero immediately

35 What is the probability of finding the particle at the walls of a rigid box?

A. 1
B. 0.5
C.
D. Infinite

36 For the ground state () of a particle in a box of length , the probability of finding the particle is maximum at:

A.
B.
C.
D.

37 The energy of the second excited state for a particle in a box corresponds to which value of ?

A. n = 1
B. n = 2
C. n = 3
D. n = 4

38 If the phase velocity of a matter wave is and the particle velocity is , then:

A.
B.
C.
D.

39 Which of the following equations represents the Schrodinger Time-Dependent equation?

A.
B.
C.
D.

40 In the normalization constant for a particle in a box, the unit of the wave function in 1D is:

A.
B.
C.
D. No units

41 Which experiment verified the wave nature of electrons?

A. Michelson-Morley Experiment
B. Davisson-Germer Experiment
C. Rutherford Scattering
D. Millikan's Oil Drop Experiment

42 For a particle in a box, the number of nodes (points of zero probability inside the box) for the -th state is:

A.
B.
C.
D.

43 The phase velocity of de Broglie waves associated with a moving particle is always:

A. Equal to the speed of light
B. Less than the speed of light
C. Greater than the speed of light
D. Zero

44 The operator for Kinetic Energy in Quantum Mechanics is:

A.
B.
C.
D.

45 If the uncertainty in the position of a particle is zero, the uncertainty in its momentum is:

A. Zero
B. Finite
C. Infinite
D.

46 Which of the following is NOT a property of the wave function ?

A. It can be a complex number.
B. It must be quadratically integrable.
C. It represents the physical trajectory of the particle.
D. It contains all information about the system.

47 The concept of 'Wave Packet' is introduced to resolve the issue that:

A. Phase velocity is greater than light velocity.
B. Group velocity is zero.
C. Waves cannot transport energy.
D. Particles have no mass.

48 Two particles have the same de Broglie wavelength. They must have the same:

A. Mass
B. Velocity
C. Momentum
D. Kinetic Energy

49 The energy difference between consecutive energy levels of a particle in a box depends on as:

A.
B.
C.
D.

50 If a proton and an electron have the same kinetic energy, which has the shorter wavelength?

A. Electron
B. Proton
C. Both have the same wavelength
D. Depends on the charge