Engineering Physics Multiple Choice Questions on “Quantum Nature of Elastic Waves”.
1. Elastic waves in crystals are made up of _______________
a) Photons
b) Nano particles
c) Atoms
d) Phonons
Answer: d
Clarification: In a crystal, when energy is provided, the lattice absorbs energy and gets excited to a higher state. When it de-excites to ground state, it releases radiation in sound-wave region, known as phonons. These waves are quantized.
2. The energy of elastic waves is given by _____________
a) nω
b) n ħω
c) nħω/2
d) (n + 1⁄2)ħω
Answer: d
Clarification: The energy of a lattice vibration is quantized which is given by the expression: E = (n + ½)ħω, where w is the angular frequency of the waves.
3. Waves in the wave packets are such that they interfere constructively over a large region of space.
a) True
b) False
Answer: b
Clarification: A wave packet consists of a group of waves, each of which have phases and amplitudes such that they interfere constructively over a small region of space where the particle can be located. Outside that region, they interfere destructively.
4. Which of the following is the correct expression for the group velocity?
a) υλ
b) dω/dυ
c) dE/dk
d) dE/ħdk
Answer: d
Clarification: The velocity with which the wave packet moves is called the group velocity. It is equal to dω/dk, which can be further simplified to dE/ħdk, as E =ħω.
5. Which of the following is the correct relation between the group velocity and the phase velocity?
a) vg = vp + λdvp/dλ
b) vp = vg + λdvp/dλ
c) vp = vg – λdvp/dλ
d) vg = vp – λdvp/dλ
Answer: d
Clarification: The relation between the phase velocity and the group velocity is given by: vg = vp – λdvp/dλ. Thus, when dvp/dλ = 0, vg = vp.
6. The motion of a wave packet is similar to _____________
a) Photons
b) Waves
c) Classical Particle
d) Quantum Particle
Answer: c
Clarification: The motion of a material/classical particle is equivalent to a group of waves or a wave packet. Such an expression can be derived by using the basic principles of motion.
7. Which of the following is not a characteristic of wave function?
a) Continuous
b) Single valued
c) Differentiable
d) Physically Significant
Answer: d
Clarification: The wave function has no physical significance. It merely helps in determining the state of a particle. It is the square of the wave function that has a physical significance.
8. There is an inextensible string of linear density µ. If it is given that ω = (ksqrt{frac{T}{μ}}), then what is the group velocity of the string?
a) (sqrt{frac{T}{μ}})
b) ħ(sqrt{frac{T}{μ}})
c) (frac{hbar}{2}sqrt{frac{T}{μ}})
d) (frac{1}{hbar}sqrt{frac{T}{μ}})
Answer: a
Clarification: As we know, vg = dω/dk
Therefore, vg = d( k(sqrt{frac{T}{μ}}))/dk
= (sqrt{frac{T}{μ}}).
9. Ψ must be normalizable.
a) True
b) False
Answer: a
Clarification: Ψ must fo to 0 as x-> infinity, y-> infinity and z -> infinity in order that ∫|Ψ|2 dv all over space be a finite constant. Thus, Ψ must be normalizable.
10. Calculate the minimum uncertainty in the momentum of a 4He atom confined to 0.40 nm.
a) 2.02 X 10-25 kg m/s
b) 2.53 X 10-25 kg m/s
c) 2.64 X 10-25 kg m/s
d) 2.89 X 10-25 kg m/s
