1 $Which experiment historically established the particle nature of light?$

A.

Interference

B.

Diffraction

C.

Photoelectric Effect

D.

Polarization

2 $According to Planck's hypothesis, energy is emitted or absorbed in discrete packets called quanta. The energy of a quantum is given by:$

A.

B.

C.

D.

3 $In the photoelectric effect, the minimum energy required to remove an electron from the surface of a metal is called:$

A.

Kinetic Energy

B.

Potential Energy

C.

Stopping Potential

D.

Work Function

4 $The Einstein's photoelectric equation is given by (where is maximum kinetic energy, is frequency, and is work function):$

A.

B.

C.

D.

5 $The de Broglie wavelength associated with a particle of momentum is given by:$

A.

B.

C.

D.

6 $If the velocity of a particle is doubled, its de Broglie wavelength will:$

A.

Double

B.

Remain the same

C.

Become half

D.

Become four times

7 $The de Broglie wavelength of an electron accelerated through a potential difference of volts is approximately given by:$

A.

B.

C.

D.

8 $Which of the following bodies will have the shortest de Broglie wavelength if they all move with the same velocity?$

A.

Electron

B.

Proton

C.

Neutron

D.

Alpha particle

9 $The de Broglie wavelength of a gas molecule at absolute temperature is given by:$

A.

B.

C.

D.

10 $The Heisenberg Uncertainty Principle states that the product of uncertainties in position () and momentum () is always:$

A.

B.

C.

D.

11 $Why is the wave nature of a moving cricket ball not observed in daily life?$

A.

Its velocity is too high

B.

Its mass is too large, making negligible

C.

It is not a charged particle

D.

It does not satisfy Planck's law

12 $The Heisenberg uncertainty principle explains why:$

A.

Electrons orbit the nucleus

B.

Electrons cannot exist inside the nucleus

C.

Protons repel each other

D.

Light travels at speed c

13 $Another form of Heisenberg's uncertainty principle relates Energy () and Time () as:$

A.

B.

C.

D.

14 $The velocity with which the envelope of a wave packet moves is called:$

A.

Phase velocity

B.

Group velocity

C.

Light velocity

D.

Sound velocity

15 $The phase velocity () is given by the relation:$

A.

B.

C.

D.

16 $For a non-relativistic material particle, the relation between group velocity () and particle velocity () is:$

A.

B.

C.

D.

17 $The phase velocity of matter waves associated with a particle moving with velocity is:$

A.

B.

C.

D.

Zero

18 $In a non-dispersive medium, the relationship between phase velocity () and group velocity () is:$

A.

B.

C.

D.

19 $The wave function in quantum mechanics represents:$

A.

The exact position of the particle

B.

The probability amplitude

C.

The energy of the particle

D.

The momentum of the particle

20 $The quantity represents:$

A.

Charge density

B.

Probability density

C.

Mass density

D.

Energy density

21 $For a wave function to be well-behaved, it must be:$

A.

Finite, continuous, and single-valued

B.

Infinite, discontinuous, and multi-valued

C.

Zero everywhere

D.

Real and positive

22 $The normalization condition for a wave function over all space is:$

A.

B.

C.

D.

23 $The operator for momentum () in one dimension is:$

A.

B.

C.

D.

24 $The operator for total energy (Hamiltonian) in the time-independent Schrodinger equation is:$

A.

B.

C.

D.

25 $Schrodinger's time-independent wave equation in one dimension is:$

A.

B.

C.

D.

26 $For a particle in a one-dimensional box of length with infinite potential walls, the potential inside the box () is:$

A.

B.

$0$

C.

D.

27 $The wave function for a particle in a 1D box of width is given by (where is an integer):$

A.

B.

C.

D.

28 $The energy eigenvalues for a particle in a 1D box of length are given by:$

A.

B.

C.

D.

29 $The lowest possible energy (Zero Point Energy) for a particle in a box corresponds to:$

A.

B.

C.

D.

30 $Which of the following statements is true for a particle in a box?$

A.

Energy levels are continuous

B.

Energy levels are discrete (quantized)

C.

The particle can be at rest ()

D.

The particle can exist outside the box

31 $The spacing between energy levels for a particle in a box:$

A.

Decreases as increases

B.

Remains constant

C.

Increases as increases

D.

Varies randomly

32 $In the Quantum Tunneling effect, a particle can cross a potential barrier even if:$

A.

Its Total Energy () is less than the Barrier Height ()

B.

C.

D.

The barrier width is infinite

33 $The probability of tunneling decreases exponentially with:$

A.

Decreasing barrier width

B.

Increasing barrier width and height

C.

Decreasing particle mass

D.

Increasing particle energy

34 $Which device works on the principle of quantum tunneling?$

A.

Scanning Tunneling Microscope (STM)

B.

Optical Fiber

C.

Laser

D.

Transformer

35 $The phenomenon of Alpha decay in radioactive nuclei is explained by:$

A.

Photoelectric effect

B.

Compton effect

C.

Quantum Tunneling

D.

Zeeman effect

36 $The Compton effect provides experimental evidence for:$

A.

Wave nature of particles

B.

Particle nature of radiation

C.

Uncertainty principle

D.

Tunneling effect

37 $The Davisson-Germer experiment confirmed the:$

A.

Particle nature of electrons

B.

Wave nature of electrons

C.

Speed of light

D.

Charge of an electron

38 $If the size of the box () is doubled, the ground state energy of the particle becomes:$

A.

Double

B.

Half

C.

Four times

D.

One-fourth

39 $In the time-dependent Schrodinger equation, the energy operator corresponds to:$

A.

B.

C.

D.

40 $A 'node' in a wave function is a point where:$

A.

Probability is maximum

B.

Probability is zero

C.

Potential energy is zero

D.

Kinetic energy is zero

41 $How many nodes (excluding boundaries) does the -th state wave function of a particle in a box have?$

A.

B.

C.

D.

42 $Two wave functions and are said to be orthogonal if:$

A.

for

B.

for

C.

D.

They have the same energy

43 $The failure of classical mechanics to explain the spectral distribution of blackbody radiation at short wavelengths is known as:$

A.

Infrared catastrophe

B.

Ultraviolet catastrophe

C.

Compton shift

D.

Stark effect

44 $In the macroscopic limit (large quantum numbers), quantum mechanics results approach classical mechanics results. This is known as:$

A.

Correspondence Principle

B.

Uncertainty Principle

C.

Exclusion Principle

D.

Superposition Principle

45 $The momentum of a photon of frequency is:$

A.

B.

C.

D.

46 $If the uncertainty in position of a particle is zero, the uncertainty in its momentum is:$

A.

Zero

B.

Infinite

C.

D.

Finite but small

47 $The stopping potential in a photoelectric experiment depends on:$

A.

Intensity of incident light

B.

Frequency of incident light

C.

Distance of light source

D.

Time of irradiation

48 $Increasing the intensity of incident light in a photoelectric experiment increases:$

A.

Kinetic energy of electrons

B.

Stopping potential

C.

Number of photoelectrons emitted

D.

Work function

49 $Matter waves are:$

A.

Electromagnetic waves

B.

Mechanical waves

C.

Probability waves

D.

Transverse waves

50 $The wavelength of a electron is approximately:$

A.

B.

C.

D.

Unit 4 - Practice Quiz