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Physics Exam Answers: Spring Semester 2005 - 6
Level One
F31SE1: From Marconi to Mars
3.
Max. data rate = 42M bits s-1.
4.
Data rate = 704 k bits s-1; Bandwidth (a) 704 kHz; (b) 704 kHz; (c) 176 kHz.
5.
D = 4625 → 4800; fref = 0.2 MHz.
6.
Min. sensitivity = 0.1 V.
7.
VSWR = 1.5 ; Power radiated by antenna = 19.2 W ; Same value of VSWR given by
a load of 33Ω. Minimum transmitter power required = 3.3W.
8.
Plasma density = 5  1014 m-3 ; Height of layer = 120 km.
F31SM3: Vibrations and Waves
1.
(a) A =
F0
M 10  i 4   2


(d) Resonance when  =
(b) Amplitude =

F0

M 10   2  16 2
2 s-1.
02 
2k 
, where 0 =
m
k
m
2.
(c) Freq. of normal modes are 0 and
3.
(a) Wavelength = 1m. (b) Wavelength = 1m. (c) =  = 4π rad. (d) v = 2ms-1.
4.
(d) k = 15 kg s-2. (f)  = 1.5 s-1.
5.
(c) c = 6 ms-1 ; (d) Mass per unit length = 0.28 Kgm-1; (e) Amplitude = 0.1 m.
(f) Wavelength = 0.4 m.
6.
(e) vg 

 ka 
 ka 
cos  ; (f) v p  0 sin   .
2
k
 2 
 2
0 a
F31SQ1: Space-Time and Matter
1.
10 years.
2.
m(v)/m0 = 3.20 ; min. freq. = 1.24  1020 Hz.
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3.
Max. kinetic energy = 1.45 eV ; Velocity = 7.14  105 ms-1.
4.
Lowest energy of neutron = 92.5 keV.
5.
Single step: E3→1 = 1.937  10-18 J ; 3→1 = 1.02  10-7 m.
Two step: 3→2 = 6.55  10-7 m.; 2→1 = 1.21  10-7 m.
6.
1
Each daughter particle has momentum Mc
2
7.
Kinetic energy (electrons) = 1100.0 eV; Kinetic energy (neutrons) = 0.60 eV.
8.
A=
  2m  2 
1  

  M  


2
; Prob. = 0.609
L
F31ST1: Thermal and Kinetic
2.
 v  nb 
 1 1
  an2     ; same as ideal gas for a = b = 0.
W  nRT ln  2
 v1  nb 
 V1 V2 
3.
From given data, kB = 1.36  10-23 JK-1.
4.
STotal = 728 JK-1.
5.
Total rate of heat flow = 6.25 W ; Temperature at junction = 20.6C.
6.
Fraction of C due to vib. modes: CO2 – 27% ; SO2 – 21%.
7.
Total work done during cycle = - 6.563 kJ.
8.
(b) EA = EB = 5ε ; B is most probable; (c) T = 295 K
F31SV1:Environmental Physics
4.
Flow rate = 2.08 m3s-1.
6.
Solar constant (Venus) = 2639 Wm-2. Net flux = 478 Wm-2 ; Equil. T = 303 K;
Fractional increase in T for new Albedo is ).66%.
7.
Fraction of land area required is about 40%.
8.
Energy released = 196 MeV.
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Level Two
F32SA5: The Structure of Galaxies
2.
(b) E = ½Mfuel c2 ; (c) Rate of mass accretion = 1.3  10-3 M๏ year-1.
6.
 R 
  9  109 M๏.
(b) Rmin = R0 sin l ; M (<R) = 
K 
 pc 
7.
(b) No escape ; (c) M (r) = 4πmkr ; (d) Vc2 (r) = 4πGmk.
8.
(d) Distance = 19 Mpc.
F32SB3: Molecular Biophysics
1.
Data suggests that AT and GC occur as base pairs.
4.
Radius of molecules = 3.98  10-9 m.
5.
[D] = 1.35mM at 37C and 0.83mM at 2C.
6.
a = 1.33 nm. ; A is simple cubic and B is face-centred cubic.
8.
Max. tensile force = 9.2  10-9 N.
F32SO1: Optics
2.
  32.4 nm.
3.
Lines per metre = 1.82  105 m-1 ; optimum blaze angle  7.
4.
fsr = 0.018 nm. ; min = 6  10-4 nm.
5.
System resolution = 2  105 lines per metre ; PSF width  5  10-6 m.;
contrast ratio is 60%.
6.
Effective focal length = 0.75 m.
7.
Assuming  = 650 nm., thickness of CeF3 and ZrO2 coatings are 98.5nm and
77.4 nm resp. Reflectance = 0.0012
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F32YQ1: Quantum Physics
1.
x  57.9 nm. ; E = 569.4 eV.
5.
m
me2
α=
; E10   2
2
2
40
6.
Energy splitting = ½ λ.
7.
(b) Transmitted flux =
9.
4r 2 a 0
Prob. of finding electron between r and r +dr is 3 e dr ;
a0
 e2 


4

0 

k 2
C ;
me
2
T
4k
  k 2
2 r
3
e2
(a) <r> = a0 ; (b) <V(r)> = 
.
2
40 a0
Results of measurement of z compt. of angular momentum are 2ħ with a
probability of ½ in each case.
10.
Given configuration gives rise to the following multiplets:
3
F4, 3F3, 3F2, 1F3, 3D3, 3D2, 3D1, 1D2, 3P2, 3P1, 3P0, 1P1.
11.
Value of Z for most stable isotope for A =120 is Z = 51.
F32ST2 Thermal and Statistical Physics
1.
TV1/3 = constant; Radius of bubble for explosion = 1.33mm.
2.
Photon energy = 3.97  10-19 J. ; S = 9.9  10-22 JK-1 ; W/Wi = exp (72).
3.

k BT
 0.038 ; Z = 26.3
4.
Prob. of Cu on lattice site is 0.6 ; Entropy of system: SN = 0.673 NkB.
5.
rev = 0.44 ;  (inventor’s engine) = 0.46
6.
4
2 / 3
(b) T   S  S0 
.
9
7.
(b) Work done by system =  mC 2T1iT2i 

47
1/ 2
 T1i  T2i

8.

U  
U 
U  U 
S  k B  N  1 
ln
 ln N  1 
  N  1ln N  1 
 ;
  
 
   

T

kB
U

1
  / k B T
;
1

N  1  N e
ln1 

 U /   
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Level Three
F33SA7: Extreme Astrophysics
3.
(b) M  108 M๏; (c) ‘a’ would be 10 times higher and there would be no change in ‘b’
5.
(a) (i) Blackbody ; (ii) Line emission ; (iii) Blackbody ; (iv) Synchrotron.
6.
(d) INS < IWD (M=0.5M๏) < IWD (M=1.0M๏).
8.
(d) M  1.7  107 M๏ ; (e) effects of relativistic beaming expected.
F33SB5: Diagnostic Medical Physics (Non-Ionising Radiation)
1.
Flip angle = 27 .
4.
R1 = 6.2 s-1mM-1 ; T1 (tissue) = 1 s.
5.
Signal increase is 15%.
7.
Resonances separated by 120 Hz ;  = 5.09 ppm ; this would change to 4.55ppm for
pH of 6.8.
8.
(b)(iii) (a) Br  -87fT ; dBr/dr  -1.3  104 fTm-1 ; (b) Br  -0.34fT ; dBr/dr  -13fTm-1.
F33SN5: Theoretical Elementary Particle Physics
1.
Mass of + = 780MeV.
6.
(c) M  2 GeV.
7.
(a) E = 5.1 eV ; (b) 1st state: J = 0, P = -1, C = +1 ; 2nd state: J = 1, P = -1, C = -1.
(d)  (2)/ (3)  137
8.
(b) Oscillator length  1600 km.
F33SO2: Laser Physics and Matter-Light Interactions
1.
(a) vp = 108ms-1 ; (b)  = 1.42  107 m-1 ; (c) R = 0.257 .
2.
Population difference = 8.4  1019 .
4.
Sodium becomes transparent to light below 205 nm.
49
6.
vsound = 5852 ms-1 in direction parallel to incoming photon; for new geometry,
frequency shift is 61 GHz at 22.5 to ingoing photon.
7.
d = 1.26 m. ; transmitted light is circularly polarised (clockwise looking in direction
of propagation) .
8.
Approx. number of modes in output is 3 or 4 ; Lmax = 3.34mm.
F33SQ6: Magnetic Resonance
5.
(i)  = 357 kHz ; (ii)  = 178.5 kHz ; (iii)  = 223.1 kHz.
F33SS2: Solid State Physics 2
3.
ELO = 33meV.
4.
me*/me = 0.093 ; r = 6.9 .
6.
k = 2.7π/a is equivalent to 0.7π/a in the first B.Z. ; (a) vs 
(b) TA 
C
b
;
M1  M 2 2
2C
2C
2C M1  M 2 
; TO 
; (c) TO 0 
M2
M1
M 1M 2
E
EG 3
m
 kT ln h ; when mh* = me* ,   G ; for Si, n = 1.67  1016 m-2 .
2
2 4
me
7.
=
8.
  20 nm.
F33SV3: Atmospheric Physics and Meteorology
1.
Lower level: N = 1.12  1011 m-3 ; height = 120 km. Upper level: N = 4.5  1011 m-3 ;
height = 225 km. ; Ratio = 171.
2.
112 D.U.
3.
Lower boundary at 198 km.
5.
(b) Thickness = 654 m.
50

6.
cu 
7.
T10 = 267K ; T50 = 256.1K
8.
(d) max = 6  10-5 rad s-1.
9.
I  1500 A ; q = 14.1 C ; E0 = 4.98  103 Vm-1 ; E10 = -6.9 Vm-1 ; x = 8.4 km.
k
2
l
2

; c = 0.2 ms-1 east to west.
51