<p> Physics Exam Answers: Spring Semester 2003-4</p><p>Level One</p><p>F31SA1: Introduction to Astrophysics</p><p>1. (b) T = 1400K (c) Apparent Magnitudes = 12.75</p><p>2. (c) Age estimates are 1 × 1010 years and 2 × 1010 years.</p><p>3. (a) Angular resolution = 1.8 milliarc seconds. (b) Max. distance = 11 Mpc.</p><p>5 6. (d) M = 9.3 × 10 M (e) Uncertainty is ±33%</p><p>7. (c) ~ 1 merger (d) number of galaxies ~ 120.</p><p>4c 8. (c) M  r 3 3 </p><p>F31SE1: Radio and Communications</p><p>2. D = 1000 → 1200</p><p>3. θc = 56.4˚</p><p>4. Data rate = 48 k bps ; Bandwith (a) 48 kHz; (b) 16 kHz ; Bandwidth for FM = 180 kHz</p><p>6. fc = 8 MHz ; Height of layer = 315 km. ; Skip distance = 473 km.; Max. range = 29.2 km.</p><p>7. Min. satellite transmitter power = 2.3 W ; EIRP = 104 kW; Diameter illuminated by beam = 670 km ; Data rate = 1.33Gbps.</p><p>8. R = 75 Ω or 33.3 Ω ; 96% of forward power radiated; max. length of cable = 4.9 km.; Sensitivity of receiver = 1μV</p><p>F31SM3: Vibrations and Waves</p><p>1. (b) f = 300 Hz: A = 1.07 × 10-4 m.; f = 740 Hz: A = 3.4 × 10-3 m (c) infinite amplitude. (d) A remains finite as always some damping in real system.</p><p>2. (a) A = 0.1 m. (b) λ = 5 m. (c) ω = 4π rad s-1 (d) v = 10 ms-1 (e) ρ = 0.05 kg m-1.</p><p>3. (b) f* = 2.29 Hz.</p><p>4. (c) A = a0 ; B = -u0 + γa0.</p><p>6. (c) f1 = 84Hz ; </p><p>44 F31SQ1: Space-Time and Matter</p><p> v 2 1  4c 2 2. v΄ = -v/2 ; m0  4m0 . v 2 1 c 2</p><p>-12 3. λmax = 1.21 × 10 m.</p><p>4. Recoil vel. = 2.94 × 10-2 ms-1 ; δE = 3.4 × 10-19 J = 2.1 eV.</p><p>1 C  5. 1 1 .  4 l 2</p><p>7. (a) Time interval: (Space station) = 2.25 × 10-7 s.; (Rocket) = 3.75 × 10-7 s. (b) Time for light pulse: (Space station) = 1.0 × 10-7 s.; (Rocket) = 3.0 × 10-7 s.</p><p>2 2 8. Force = mL3</p><p>F31ST1: Thermal and Kinetic</p><p>V f  c  1. W  RT ln  ; Work on ideal gas is smaller.  Vi  c </p><p>-12 -1 -12 -1 -14 -1 4. ΔS1 = -3.6496 × 10 JK ; ΔS2 = +3.6630 × 10 JK ; net change = +1.34 × 10 JK ; 8 Change in number of accessible states Ωf/ Ωi = exp(9.7 × 10 ) .</p><p>3 5. ΔVAB = 2 m ; net change in internal energy round cycle is zero.</p><p>-1 -1 6. (i) Q = 29.3 kJ ; (ii) cmaterial = 861 J kg K so material is not Copper; -1 -1 -1 (iii) ΔSdisc = -76.6 J K ; (iv) κwood = 0.0714 W m K ; (v) Thickness of Cu = 112 m.</p><p>7. (a) T = 353K after adiabatic expansion; (b) ΔQ = 1870 J ; 0 J; -1662 J resp.; ΔW = 0 J; -891 J; 667 J resp.; ΔU = 1870J; -891 J; -995 J resp. (c) efficiency = 11%; (d) Efficiency (Carnot) = 35%.</p><p>8. (a) CO2 molecule has 4 vibrational degrees of freedom; (b) each contributes RT to total energy; (c) He gas; (e) agreement between expt. and equipartition theory best at high T .</p><p>45 Level Two</p><p>F32SA5: The Structure of Galaxies</p><p>  z 2    exp  1. 0  2   2 </p><p>-4 3. (c) Rate of accretion = 1.3 × 10 M per year.</p><p>1 4. (b) 2 2 2 IR  2i0 r 0  R </p><p>F32SB4: Molecular Biophysics</p><p>2. Number of generations = 11.</p><p>3. Maximum tensile force = 9.2 × 10-9 N.</p><p>4. (a) Time elapsed between mutations of order 1055 s. (b) Min number of atoms = 1030.</p><p>5. (b) Equilibrium coefficient = 2.85 × 10-3 .</p><p>6. F100 = 0 ; F110 = 2f ; F111 = 0 ; Phase angle = ± 31.3°.</p><p>7. Frequency separation: (500MHz) 300 Hz; (900MHz) 540 Hz.</p><p>8. (d) Oxygen delivered = 2.98 × 10-3 Moles.</p><p>F32SO1: Optics</p><p>2. (a) d ~ 15.8 μm; (b) N = 10; (c) a = 5.04 μm.</p><p>3. Resolution limit =12.5 μm; Width of PSF = 25 μm; Contrast ratio : 15%.</p><p> a 4. Intensity is zero for all u except u =  2</p><p>5. One mode.</p><p>6. Angular magnification of telescope is –250.</p><p>7. T (GaAs) = 0.714; Coating thickness = 2.4 × 10-7 m. ; T (coated surface) = 0.98</p><p>8. lmax = 1.9 mm.; wmax = 1 mm.</p><p>46 F32SQ2: Quantum Physics 2</p><p>3. Splitting = 3λ/2;</p><p>6. Quantum numbers for system are l = 2 and ml = ±2.</p><p>3 1 3 3 3 1 7. 4s4f has terms F and F with multiplets F4, F3, F2 ; F3. 3 1 3 3 3 1 4s4d has terms D and D with multiplets D3, D2, D1 ; D2. 3 3 3 3 F4 and F3 are separated by 4λ1 and F3 and F2 by 3λ1 where λ1 is the spin-orbit 3 3 3 3 3 coupling constant for F. D3 and D2 are separated by 3λ2 and D2 and D1 by 2λ2 where λ2 3 is the spin-orbit coupling constant for D.</p><p>8. J = 4.27 eV; K = 0.1 eV.</p><p>F32YT2 Thermal and Statistical Physics</p><p>2. Probability = 0.2325</p><p>4. Work = 1220 J.</p><p> nRT 2U 5. P  ; T  . V 5Rn</p><p> N 2 e kBT c  2  2 6. (b) k BT   . e kBT 1    </p><p>8. Radius of bubble = 1.09 × 10-3 m. ; Pressure = 439 pi.</p><p>Level Three</p><p>F33SA7: Extreme Astrophysics</p><p>1   2 2. (b) 3 .      4 T ne r </p><p>3. (a) 2.6 × 1046 J. ; (b) 9 × 1044 J.; (c) 4 × 1044 J.</p><p>4. (b) r* = 6 km.</p><p>47 9 6 5. (a) T = 10 K ; (c) M = 5 × 10 M .</p><p>6. (d) Frequency = 3 GHz; (e) Average frequency = 23 GHz;</p><p>8. (e) Change in frequency = 1 × 10-5 .</p><p>F33SB6: Functional Imaging</p><p>4. Signal change = 13.3 %</p><p>8. (c) (i) Gradient (8cm) = 100 fT cm-1; (ii) Gradient (2cm) = 1.6fT cm-1. Number of evoked responses = 400. </p><p>F33SN5: Theoretical Elementary Particle Physics</p><p>1 2 Gme -43  c  2 -8 5. (a) αG = ~ 10 . (b) = 2.17 × 10 kg. M P    c  G </p><p>6. (d) R (1GeV) = 2 ; R (20GeV) =11/3. (g) CF = ⅓.</p><p>7. (d) Δm  6 × 10-13 MeV; Next value of equality is at x = 150 cm.</p><p>F33SQ6: Magnetic Resonance</p><p>4. Proton-proton distance is 1.57 × 10-10 m.</p><p>-9 5. (b) τc = 7.58 × 10 s. ; Brms = 0.50 mT.</p><p>8 -1 -1 -1 8 -1 6. (b) E1 = (-3 × 10 + 16) s ; E2 = -18.42 s ; E3 = 10.42 s ; E4 = (3 × 10 - 8) s . (c) Allowed transitions are E2 – E1, E3 – E1, E4 – E3, E4 – E2.</p><p>8. (a) (ii) Mx = M0 sin ωLt exp (-t/T2) ; My = M0 cos ωLt exp (-t/T2) ; Mz = M0 (1- exp (-t/T1) ;</p><p>F33SS3: Solid State Physics III</p><p>2. χ (100˚C) = 0.031 </p><p>-1 3. vc = 14.3 m s .</p><p>7. Mean molecular field = 1.02 × 103 T.</p><p>4 -1 8. For magnon vg max = 2.43 × 10 m s at λ = 1.6 nm.</p><p>48 F33SS4: Semiconductor Physics and Devices</p><p>6. Flux (100) = 6.26 × 1018 atoms/m2 ; Flux (110) = 4.43 × 1018 atoms/m2 ; (b) GR (100) = 1.017 μm/hour ; GR (110) = 0.719 μm/hour ;</p><p>7. Vbi = 0.794 V.</p><p>8. Schottky barrier height = 0.65 eV; Vbi = 0.61 eV; Pinch-off voltage = 25.62V; Min. thickness = 9.16 × 10-6 cm.; Thickness for depletion mode device = 2.78 × 10-5 cm. </p><p>F33ST6: Quantum Coherence</p><p>1. Density = 1.27 × 108 m-2.</p><p>4. Fermi energy = 5.49 × 1022 J.</p><p>6. Field change = 1.05nT</p><p>7. (d) Sheet density = 2.4 × 1015 m-2.</p><p>F33SV3: Atmospheric Physics and Meteorology</p><p>3. Ozone in Dobson units = 187 D.U.</p><p>5. Atmos pressure of CO2 required = 56 kPa.</p><p>6. zc (Jupiter) = 670 km.</p><p>7. For layer at 113km, N = 7.76 × 1010 electrons/m3 For layer at 210 km, N = 3.76 × 1011 electrons/m3.</p><p>9. (e) umax = ug as z goes to ; vmax = 0.32 ug at z = 513 m.</p><p>49</p>