1 $Which of the following phenomena could NOT be explained by classical mechanics, leading to the development of quantum mechanics?$

A.

Interference of light

B.

Diffraction of light

C.

Black body radiation

D.

Polarization of light

2 $In the photoelectric effect, the emission of electrons from a metal surface occurs only when the incident light has a frequency:$

A.

Less than the threshold frequency

B.

Equal to or greater than the threshold frequency

C.

Equal to the speed of light

D.

Independent of frequency

3 $According to Einstein's photoelectric equation, the maximum kinetic energy () of the emitted photoelectron is given by:$

A.

B.

C.

D.

4 $The work function of a material is defined as:$

A.

The maximum energy required to remove an electron

B.

The minimum energy required to remove an electron from the surface

C.

The total energy of the electron in the atom

D.

The kinetic energy of the incident photon

5 $In the photoelectric effect, if the intensity of incident light is increased while keeping the frequency constant:$

A.

The maximum kinetic energy of photoelectrons increases

B.

The stopping potential increases

C.

The photoelectric current increases

D.

The threshold frequency decreases

6 $The concept of matter waves was proposed by:$

A.

Werner Heisenberg

B.

Erwin Schrodinger

C.

Louis de Broglie

D.

Max Planck

7 $The de Broglie wavelength () of a particle with momentum is given by:$

A.

B.

C.

D.

8 $If a proton and an electron have the same velocity, which one has the shorter de Broglie wavelength?$

A.

Electron

B.

Proton

C.

Both have the same wavelength

D.

Cannot be determined

9 $The de Broglie wavelength of a particle of mass and kinetic energy is:$

A.

B.

C.

D.

10 $Calculate the de Broglie wavelength of an electron accelerated through a potential difference of volts (approximate formula).$

A.

nm

B.

nm

C.

nm

D.

nm

11 $Which experiment provided the first experimental proof of the wave nature of electrons?$

A.

Michelson-Morley Experiment

B.

Davisson-Germer Experiment

C.

Rutherford Scattering Experiment

D.

Millikan's Oil Drop Experiment

12 $Why are wave properties not observed in macroscopic objects like a moving cricket ball?$

A.

Their velocity is too high

B.

Their mass is too small

C.

Their wavelength is negligibly small

D.

They do not possess momentum

13 $Heisenberg's Uncertainty Principle states that it is impossible to simultaneously measure precisely the:$

A.

Mass and velocity of a particle

B.

Charge and position of a particle

C.

Position and momentum of a particle

D.

Energy and charge of a particle

14 $The mathematical expression for Heisenberg's Uncertainty Principle involving energy () and time () is:$

A.

B.

C.

D.

15 $Based on the Uncertainty Principle, why can an electron NOT exist inside the nucleus?$

A.

The nucleus is positively charged

B.

The required kinetic energy would be impossibly high

C.

The mass of the electron is too small

D.

The electron would repel the protons

16 $If the uncertainty in the position of a particle is zero, the uncertainty in its momentum is:$

A.

Zero

B.

Finite

C.

Infinite

D.

Negative

17 $The velocity with which a single monochromatic wave travels is called:$

A.

Group velocity

B.

Phase velocity

C.

Particle velocity

D.

Drift velocity

18 $Group velocity () is defined as:$

A.

B.

C.

D.

19 $In a non-dispersive medium, the relation between phase velocity () and group velocity () is:$

A.

B.

C.

D.

20 $For a material particle in motion, the group velocity of the matter waves associated with it is equal to:$

A.

The speed of light ()

B.

The phase velocity ()

C.

The particle velocity ()

D.

Zero

21 $The phase velocity of de Broglie waves associated with a moving particle () is:$

A.

Always less than

B.

Always equal to

C.

Always greater than

D.

Equal to particle velocity

22 $The relation between group velocity () and phase velocity () in a dispersive medium is:$

A.

B.

C.

D.

23 $The wave function in quantum mechanics represents:$

A.

The exact position of the particle

B.

The exact momentum of the particle

C.

The state of the system

D.

The energy of the particle

24 $According to Max Born's interpretation, the quantity (or) represents:$

A.

Charge density

B.

Probability density

C.

Mass density

D.

Energy density

25 $The normalization condition for a wave function over all space is:$

A.

B.

C.

D.

26 $Which of the following is NOT a requirement for a well-behaved (acceptable) wave function?$

A.

It must be single-valued

B.

It must be finite everywhere

C.

It must be continuous

D.

It must be constant everywhere

27 $The time-dependent Schrodinger equation for 1D motion is:$

A.

B.

C.

D.

28 $The time-independent Schrodinger equation allows us to find:$

A.

The future position of a particle

B.

The stationary energy states (eigenvalues) and wave functions

C.

The exact path of the particle

D.

The relativistic mass

29 $In the Schrodinger equation, the operator for total energy (Hamiltonian) is:$

A.

B.

C.

D.

30 $The operator for momentum () in quantum mechanics is:$

A.

B.

C.

D.

31 $For a 'Particle in a 1D Box' of length, the potential inside the box () is:$

A.

Infinite

B.

Zero

C.

Constant (non-zero)

D.

Variable

32 $For a particle in a 1D box of length, the potential outside the box is:$

A.

Zero

B.

Infinite

C.

D.

Negative

33 $The energy eigenvalues for a particle in a 1D box of width are given by ():$

A.

B.

C.

D.

34 $The lowest possible energy (Ground state,) of a particle in a box is:$

A.

Zero

B.

C.

Infinite

D.

35 $The wave function for a particle in a 1D box of length is of the form:$

A.

B.

C.

D.

36 $What is the value of the normalization constant for a particle in a box of length ?$

A.

B.

C.

D.

37 $The energy levels of a particle in a 1D box are:$

A.

Continuous

B.

Discrete and equally spaced

C.

Discrete and not equally spaced

D.

Random

38 $If the length of the box is doubled, the ground state energy of the particle:$

A.

Doubles

B.

Becomes half

C.

Becomes one-fourth

D.

Remains same

39 $The number of nodes (points where inside the box) for the -th quantum state is:$

A.

B.

C.

D.

40 $The Quantum Tunneling effect is a phenomenon where a particle can cross a potential barrier even if:$

A.

Its energy is greater than the barrier height ()

B.

Its energy is less than the barrier height ()

C.

Its mass is zero

D.

It has no charge

41 $Which of the following devices works on the principle of quantum tunneling?$

A.

Optical Fibre

B.

Scanning Tunneling Microscope (STM)

C.

He-Ne Laser

D.

Hydraulic Press

42 $In the tunneling effect, the probability of tunneling decreases exponentially with:$

A.

Decreasing barrier width

B.

Increasing barrier width and height

C.

Increasing particle energy

D.

Decreasing mass of particle

43 $What is the physical significance of the 'Zero Point Energy' in a particle in a box?$

A.

The particle is at rest

B.

The particle can never be at complete rest

C.

The potential energy is zero

D.

The box has no boundaries

44 $For a free particle (potential everywhere), the energy spectrum is:$

A.

Discrete

B.

Continuous

C.

Zero

D.

Negative

45 $The probability of finding a particle in a 1D box is maximum at the center for which state?$

A.

(Ground state)

B.

C.

D.

46 $Alpha decay in radioactive nuclei is an example of:$

A.

Photoelectric effect

B.

Compton effect

C.

Quantum Tunneling

D.

Zeeman effect

47 $The Laplacian operator in Cartesian coordinates is:$

A.

B.

C.

D.

48 $In the relation, the constant is:$

A.

Boltzmann constant

B.

Planck's constant

C.

Rydberg constant

D.

Stefan's constant

49 $Which of the following properties implies that the Schrodinger equation is linear?$

A.

If and are solutions, then is also a solution

B.

The probability is

C.

Energy is conserved

D.

The potential is constant

50 $The de Broglie wavelength of a neutron at thermal equilibrium at temperature is proportional to:$

A.

B.

C.

D.

Unit 4 - Practice Quiz