# Semiconducter Devices And Circuit :-Semiconducter Assignment 1 Answers

## 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.

a) (i)

b) (ii)

c) (iii)

(a) 2

(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)

a) 0.225 nm

c) 22.5 nm

d) 0.02 nm

b) 1

c) 2/𝐿

d) √15 𝐿 −3/5

b) zero

c) 0.024

d) 0.0063

### 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.

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’?

(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) −( ℏ2)/ ma  (Answer)

d) − 2ma/( ℏ ^2)