Unit 4 - Practice Quiz

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

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 ?

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:

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

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

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

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

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

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

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

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

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

13 Group velocity () is defined mathematically as:

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

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

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

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

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

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

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

21 A wave function in quantum mechanics represents:

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

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

24 The condition is known as the:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

41 Which experiment verified the wave nature of electrons?

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

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

44 The operator for Kinetic Energy in Quantum Mechanics is:

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

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

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

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

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

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