Contents:-

- 1 WEEK 1 – Excursion in Quantum Mechanics
- 1.1 1. The wave-function of the particle must be “normalizable”, because
- 1.2 2. Which of the following is not a valid quantum mechanical wave-function?
- 1.3 3. If the ratio of maximum and minimum intensities in an interference pattern is 25:1 then the ratio of amplitudes of two interfering waves will be
- 1.4 4. In electron beam lithography patterns are exposed with electrons. The small wavelength of electrons helps to achieve small feature sizes (in order of nm). Assume an electron gun of energy 50 keV. What is the wavelength of these electrons? Assume the mass of electron = 9.109 × 10−31 kg and Planck’s constant, h = 6.626 × 10−34 J.s. Neglect the relativistic effect.
- 1.5 5. An electron in an infinite one-dimensional potential well jumps from the n = 4 energy level to the ground state energy level and in doing so emits a photon of wave-length 20.9 nm. What is the width of the well? Assume electron mass = 9.11e − 31 kg, ℎ = 6.626e − 34 J. s and c = 3e8 m/s.
- 1.6 6. A wave function is given by ψ(x) = 0 if, 𝑥 < 0 = (A√30)𝑥(L − 𝑥) if, 0 ≤ 𝑥 ≤ L = 0 if, 𝑥 > L what is value of A?
- 1.7 7. An electron is bound in an infinite 1-d potential well of width 7.3nm along the xaxis. The system is at state n =3.The probability of finding the electron per nm length at x = 0.3 nm is closest to
- 1.8 8. Electrons are accelerated through an electric potential V and then fall on a pair of slits that have a separation of 100 nm. The resultant interference pattern indicates that the electrons have a wavelength of 1 nm.
- 1.9 i) What is the value of the accelerating electric potential V?
- 1.10 ii) After passing through the slits what is the minimum spread in the electron’s momentum in the direction parallel to the plane of the slits and perpendicular to the average path of the electrons? Assume ℎ = 6.626 × 10−34 J.s and electron mass, m = 9.11 × 10−31 kg. Ignore any relativistic effect.
- 1.11 9. The wave-function of a particle at state ‘n’ is given by, ψ(x) = √ 3 cos( 2𝜋x /a ), |x| ≤ a/2 0, |x| > a/2 What is the average momentum of the particle at the state ‘n’?
- 1.12 10. Consider a particle of mass m moving in the one-dimensional potential V(x) = A𝛿(x) for |x| < a and V(x) = ∞ elsewhere. The value of A for which the ground state energy of the system vanishes is

- 2 DOWNLOAD PDF

**WEEK 1 – Excursion in Quantum Mechanics**

In this blog we are providing semiconducter assignment 1 answers of NPTEL/SWAYAM. We will provide answers of every week of nptel courses.

### 1**. The wave-function of the particle must be “normalizable”, because **

a) the particle’s momentum must be conserved.

b) the particle can not exist at two places at the same time.

**c)the particle must exist somewhere in the space. (Answer)**

d)the particle’s charge must be conserved.

**2. Which of the following is not a valid quantum mechanical wave-function?**

a) (i)

b) (ii)

c) (iii)

**d) (iv)** **(Answer)**

**3. If the** **ratio of maximum and minimum intensities in an interference pattern is 25:1 then the ratio of amplitudes of two interfering waves will b**e

(a) 2

**(b) 1.5 (Answer) **

(c) 5

(d) 2.5

**4. In electron beam lithography patterns are exposed with electrons. The small wavelength of electrons helps to achieve small feature sizes (in order of nm). Assume an electron gun of energy 50 keV. What is the wavelength of these electrons? Assume the mass of electron = 9.109 × 10−31 kg and Planck’s constant, h = 6.626 × 10−34 J.s. Neglect the relativistic effect. **

a) 5.5 nm

b) 0.0039 nm

c) 3.9 nm

**d) 0.0055 nm (Answer)**

**5. An electron in an infinite one-dimensional potential well jumps from the n = 4 energy level to the ground state energy level and in doing so emits a photon of wave-length 20.9 nm. What is the width of the well? Assume electron mass = 9.11e − 31 kg, ℎ = 6.626e − 34 J. s and c = 3e8 m/s. **

a) 0.225 nm

**b) 0.308nm (Answer)**

c) 22.5 nm

d) 0.02 nm

**6. A wave function is given by ψ(x) = 0 if, 𝑥 < 0 = (A√30)𝑥(L − 𝑥) if, 0 ≤ 𝑥 ≤ L = 0 if, 𝑥 > L **

what is value of A?

what is value of A?

**a) 𝐿 ^{−5/2}**

**(Answer)**

b) 1

c) 2/𝐿

d) √15 𝐿 ^{−3/5}

**7. An electron is bound in an infinite 1-d potential well of width 7.3nm along the xaxis. The system is at state n =3.The probability of finding the electron per nm length at x = 0.3 nm is closest to **

** a) 0.039 (Answer) **

b) zero

c) 0.024

d) 0.0063

### 8. **Electrons are accelerated through an electric potential V and then fall on a pair of slits that have a separation of 100 nm. The resultant interference pattern indicates that the electrons have a wavelength of 1 nm. **

**i) What is the value of the accelerating electric potential V? **

**ii) After passing through the slits what is the minimum spread in the electron’s momentum in the direction parallel to the plane of the slits and perpendicular to the average path of the electrons? Assume ℎ = 6.626 × 10**^{−34} J.s and electron mass, m = 9.11 × 10^{−31} kg. Ignore any relativistic effect.

^{−34}J.s and electron mass, m = 9.11 × 10

^{−31}kg. Ignore any relativistic effect.

a) i) 1 V ii) infinity

b) i) 1 V ii) zero

c) i) 1.5 V ii) 10.54e-28 kg.m/s

**d) None of these** ** (Answer) **

### 9. **The wave-function of a particle at state ‘n’ is given by, ψ(x) = √ 3 cos( 2𝜋x /a ), |x| ≤ a/2 0, |x| > a/2 What is the average momentum of the particle at the state ‘n’? **

**(a) zero (Answer) **

(b) 6ℏ𝜋/a

(c) ℏ𝜋/a

(d) none of these

**10. Consider a particle of mass m moving in the one-dimensional potential V(x) = A𝛿(x) for |x| < a and V(x) = ∞ elsewhere. The value of A for which the ground state energy of the system vanishes is **

a) 0

b) (ℏ ^2)/ ma

**c) −( ℏ ^{2})/ ma (Answer) **

d) − 2ma/( ℏ ^2)

## DOWNLOAD PDF

semiconducter assignment 1 answers, semi conducter answers