Indian Institute of Information Technology Una Assignment-02 PDF

Indian Institute of Information Technology Una...

Indian Institute of Information Technology Una Himachal Pradesh (An Institute of National Importance under MoE) Saloh, Una - 177 209, India Website: www.iiitu.ac.in AY 2024-25 ASSIGNMENT-II B. Tech. (I Semester) Branch: ECE/IT Subject: ICMD103 (Engineering Physics) Date: 02/12/2024 Q.1: Make use of commutator algebra, and show that: [Jˆx , [Jˆy , Jˆz ]] + [Jˆy , [Jˆz , Jˆx ]] + [Jˆz , [Jˆx , Jˆy ]] = 0. 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 Q.2: Compare the relative probabilities of spontaneous and stimulated emission in an equilibrium system at room temperature (T =350K) for transitions that occur in the visible (hν = 2.5eV) and the microwave regions (hν = 10-5 eV) of the spectrum. Q.3: Compute the probability current density for a Gaussian wave packet: x2 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 + }i p0 x (x) = Ae a2 and compare with the classical relation J = ρv. Q.4: The Hall coefficient and electrical conductivity of silicon are -7.2×10-5 m3/C and 1.5×108 mho/m, respectively. i) Calculate the magnitude of the mobility of the electrons. ii) How many charge carriers are there in the silicon sample? iii) What is the type of semiconductor? Q.5: At what angle will a diffracted beam emerge from the (222) planes of a face centered cubic crystal of unit cell length 0.5 nm? Assume diffraction occurs in the first order and that the X-ray wavelength is 0.3 nm. Q.6: Consider the solutions of linearly polarized harmonic plane waves: ~ ~ E = E0 ei(wt k.~ r+ ) , B = B0 ei(wt k.~ r+ ) Where E0 and B0 are constant vectors associated with maximum amplitude of oscillations. Show that B and E are orthogonal fields. Q.7: The refractive index of core material of the optical fiber is 1.48. Find the refractive index of cladding material such that light rays incident at an angle grater than 12o are not reflected at the core-cladding interface and therefore not guided along the optical fiber system. *****