Engineering Physics Questions and Answers – Particle in a Box

This set of Engineering Physics Multiple Choice Questions & Answers (MCQs) focuses on “Particle in a Box”.

1. The walls of a particle in a box are supposed to be ____________
a) Small but infinitely hard
b) Infinitely large but soft
c) Soft and Small
d) Infinitely hard and infinitely large
View Answer

Answer: d
Explanation: The simplest quantum-mechanical problem is that of a particle in a box with infinitely hard walls and are infinitely large.

2. The wave function of the particle lies in which region?
a) x > 0
b) x < 0
c) 0 < X < L
d) x > L
View Answer

Answer: c
Explanation: The particle cannot exist outside the box, as it cannot have infinite amount of energy. Thus, it’s wave function is between 0 and L, where L is the length of the side of the box.

3. The particle loses energy when it collides with the wall.
a) True
b) False
View Answer

Answer: b
Explanation: The total energy of the particle inside the box remains constant. It does not loses energy when it collides with the wall.
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4. The Energy of the particle is proportional to __________
a) n
b) n-1
c) n2
d) n-2
View Answer

Answer: c
Explanation: In a particle inside a box, the energy of the particle is directly proportional to the square of the quantum state in which the particle currently is.

5. For a particle inside a box, the potential is maximum at x = ___________
a) L
b) 2L
c) L/2
d) 3L
View Answer

Answer: a
Explanation: In a box with infinitely high barriers with infinitely hard walls, the potential is infinite when x = 0 and when x = L.

6. The Eigen value of a particle in a box is ___________
a) L/2
b) 2/L
c) \(\sqrt{L/2}\)
d) \(\sqrt{2/L}\)
View Answer

Answer: d
Explanation: The wave function for the particle in a box is normalizable, when the value of the coefficient of sin is equal to \(\sqrt{2/L}\)
. It is the Eigen value of the wave function.

7. Particle in a box can never be at rest.
a) True
b) False
View Answer

Answer: a
Explanation: If the particle in a box has zero energy, it will be at rest inside the well and it violates the Heisenberg’s Uncertainty Principle. Thus, the minimum energy possessed by a particle is not equal to zero.
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8. What is the minimum Energy possessed by the particle in a box?
a) Zero
b) \(\frac{\pi^2\hbar^2}{2mL^2}\)
c) \(\frac{\pi^2\hbar^2}{2mL}\)
d) \(\frac{\pi^2\hbar}{2mL}\)
View Answer

Answer: b
Explanation: The minimum energy possessed by a particle inside a box with infinitely hard walls is equal to \(\frac{\pi^2\hbar^2}{2mL^2}\). The particle can never be at rest, as it will violate Heisenberg’s Uncertainty Principle.

9. The wave function of a particle in a box is given by ____________
a) \(\sqrt{\frac{2}{L}}sin\frac{nx}{L}\)
b) \(\sqrt{\frac{2}{L}}sin\frac{n\pi x}{L}\)
c) \(\sqrt{\frac{2}{L}}sin\frac{x}{L}\)
d) \(\sqrt{\frac{2}{L}}sin\frac{\pi x}{L}\)
View Answer

Answer: b
Explanation: The wave function for the particle in a box is given by: \(\sqrt{\frac{2}{L}}sin\frac{n\pi x}{L}\). The Energy possessed by the particle is given by: \(\frac{n^2\pi^2\hbar^2}{2mL^2}\).
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10. The wave function for which quantum state is shown in the figure?
Wave function is for 2nd principal quantum number for wave function for state when n = 2
a) 1
b) 2
c) 3
d) 4
View Answer

Answer: b
Explanation: The shown wave function is for the 2nd principal quantum number, i.e., it is the wave function for the state when n = 2.

11. Calculate the Zero-point energy for a particle in an infinite potential well for an electron confined to a 1 nm atom.
a) 3.9 X 10-29 J
b) 4.9 X 10-29 J
c) 5.9 X 10-29 J
d) 6.9 X 10-29 J
View Answer

Answer: c
Explanation: Here, m = 9.1 X 10-31 kg, L = 10-9m.
Therefore, E = \(\frac{\pi^2\hbar^2}{2mL^2}\)
= 3.14 X 3.14 X 1.05 X 1.05 X 10-68/ 2 X 9.1 X 10-31 X 10-9
= 5.9 X 10-29 J.

Sanfoundry Global Education & Learning Series – Engineering Physics.

To practice all areas of Engineering Physics, here is complete set of 1000+ Multiple Choice Questions and Answers.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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