Physics Exam Answers: Spring Semester 2004-5
Level One
F31SA1: Introduction to Astronomy
2.
(a) K = 1 ; (b) v = 13,000 m s-1.
3.
(c) t = 1.5  1014 years ; this is >> age of universe (1.5  1010 years).
4.
(c) L = 2000 L๏
6.
(d) M = 6.5 ; (e) D = 5000 pc.
7.
(d) M = 1.9  1011 M๏ ; (f) M = 1010 M๏ .
8.
(c) Emax = 1.9 ; (d) RES = 0.02 arc sec. ; (e) max = 21º .
F31SE1: Radio and Communications
1.
Minimum frequency = 23.7 MHz.
2.
Minimum transmitter power = 0.36 mW.
3.
Bandwidth needed = 24 KHz.
5.
Reference Oscillator Freq. = 0.1 MHz ; D = 880 to 1080.
6.
Proportion of total power in sidebands = 1/9 .
7.
Max. length = 1500 m. ; Max.length for single mode fibre = 10,000 m.
8.
VSWR = 1.5 ; Power = 9.6 W ; R = 33  ; 4 repeaters needed.
F31SM3: Vibrations and Waves
1.
(b)  = 10 rad s-1 ;
2.
(b) d = 5.45 cm.
3.
(a)  = 1 m. ; (b)  = 20 rad s-1 ; (c) v = 10 ms-1 ; (d)  = 0.05 Kg m-1 .
44
F31SQ1: Space-Time and Matter
1.
Ratio = 0.92 .
2.
v = 2.846  108 ms-1 .
3.
No. of photons per sec. = 3.01  1016 ; Kinetic energy = 4.18 eV.
4.
P  5.28  10-21 kg m s-1 ; K > 52.0 keV.
5.
d = 2.5  10-10 m.
6.
(a) Earth recession speed = -vA ; (b) B recession speed = 
7.
p = 3.5  10-18 Ns ; v = 2.6  108 ms-1 .
8.
Photon freq. emitted : 31 = 2.921  1015 Hz ; 32 = 4.5641  1014 Hz ; 31 =
2.46  1015 Hz ; No. of photons needed = 840.
( v A  vB )
.
1  v AvB / c 2
According to Earth observer, LA = 47.7 m. and LB = 45.8 m. According to
Rocket B observer, LA = 39.03 m.
F31ST1: Thermal and Kinetic
2.
10 ways of arranging quanta; i.e. one oscillator has 3 and the others none
(total 3); one oscillator has 2, one has 1 and the other zero (total 6); an equal
sharing among the three oscillators (total 1).
4.
Best efficiency is given by 1-(TL/TH) = 75%; so engineer's claim not valid.
5.
Work done = P0 (V2  V1 ) 
6.
AB: Q = +3740 J ; W = 0 ;
U = +3740 J.
BC: Q = 0 ;
W = -1876 J ; U = -1876 J.
CA: Q = -3220 J ; W = 1111J ; U = -1901 J.
α 2
2
(V2  V1 ) .
2
3
7.
8.
 m 2 4
(b) A = 
.

 2kT  
(b) (iii) and (iv) are possible answers;
(c) Total change (single stage) = +0.04C JK-1 ; Total change (two stage) = +0.04C JK-1
45
Level Two
F32SA5: The Structure of Galaxies
3.
8.33
.
1/ 4
Re
(b) M  1  1014 M๏ ; (c) M/L  102 M๏/L๏ .
6.
(d) Rinner = 0.7 Kpc ; (e) VLOSmax = 180 Km s-1 .
7.
(d) ΔV ≈ 106 ms-1 ; (e) R  2 × 1014 m. (g) D ≤ 50Mpc.
8.
V
(a) constant of prop. = 0 ; (c) Grav. Pot. = V02 ln r ; (d) Infinite energy.
G
1.
A  C  2.5 log 10 I e  8.33 ; B 
2
F32SB3: Molecular Biophysics
1.
r0 = 0.147  10-9 m.
2.
[DHAP] 96.26% ; [GA3P] 3.74%; Rate increased by factor of 2.344
3.
K=
4.
Separation of multiplets = 250 Hz.
5.
Net charges: low pH +2, neutral 0, high pH -2.
6.
Diffusion distance  0.9 mm. ; equilibrium current = 3.14  10-22 Mol m-2 s-1.
7.
Phase difference = a [ h + k + l ].
8.
Number of generations = 8.
S ASB
F32SO1: Optics
1.
Focal length = 0.35 m. ; lateral magnification = 2.34.
2.
Angular diameter of star   2.67  10-7 rad.
3.
Angular magnification = -20.
4.
Transmittance = 97.2 %.
6.
Image formed 0.0455 m. behind sphere; lateral magnification = -0.273 .
46
7.
Free spectral range = 0.125 Å .
8.
Distance between missing fourth order maxima = 10.92 mm. ;
Slit separation = 400 m. ; irradiance I1/I0 = 0.81 and I2/I0 = 0.405 .
F32SQ2: Quantum Physics 2
2
1.
m  e2 
me2

 .
E


Angular momentum in ground state = 0 ;  
;
1
2 2  40 
40 2
2.
2.79455 eV; 2.79460 eV; 2.79466 eV; 2.79472 eV; 2.79478 eV; 2.79484 eV;
2.79489 eV.
5.
J = 1, 2, 2 and 3. There are 3 possible transitions to a J = 3 level of another
configuration.
6.
u(x, y, z) = x + iy is an eigenfunction of L̂ z with eigenvalue +1.
For u(r, , ), Value of observable for L̂ z is -1 and for L̂2 is +2, giving l = 1.
7.
Splitting of Sodium doublet is 2.15  10-3 eV.
8.
Mass ( 168O ) = 15.9939 u . Energy to remove neutron = 16.55 MeV. Binding energy
per nucleon ( 208
82 Pb ) = 7.734 MeV/nucleon.
F32YT2 Thermal and Statistical Physics
1.
Z = 435.
2.
S = 1.11  10-22 JK-1 ; no. of accessible states changes by factor of 3139.
4.
Prob. of all six correct is 7.15  10-8 ; prob. of all six incorrect is 0.436.
5.
Latent heat of sublimation of zinc = 13  104 J mol-1.
6.
T2 = 42.86 K ; work per cycle = 8.7 J.
7.
 2 Ik T 
S = k B ln  2B   k B ; C = kB ; I = 2.8  10-47 kg m2 ; ħ2/2I = 2  10-22 J ;
  
T  13 K.
1
8.
 kEVT


 N n
 N  n 
F = nEV  k BT  N ln 
  ln 
  ; n  N  e B  1 .


 N 
 n 



47
Level Three
F33SA7: Extreme Astrophysics
3.
(a) T  2  107 K ; peak  1.5 Å.
4.
Sun: Pmin  9900 s. ; white dwarf: Pmin  15 s. ; neutron star: Pmin  0.5 ms.
5.
(b) peak, AGN = 162 Å.
6.
(b) ne  530 electrons per m3 ; Mtotal  5  1013 M๏; (c) cooling time  1011 years.
7.
(a) M < 1.4  108 M๏ ; (b) M > 7  107 M๏ ; M  1600 Earth masses per day ;
(d) Ratio of quaser energy to binding energy  800.
8.
(c) Energy = 173 KeV.
F33SB6: Functional Imaging
3.
Detector pitch = 6.
4.
(b) Mean transit time = 9.09 s.
5.
Corrected count = 2000.
6.
 = 1.12 ; Q/V = 0.554 .
8.
Volume required = 0.71 ml. ; percentage uptake = 10.3 % .
F33SN5: Theoretical Elementary Particle Physics
1.
r  4  10-16 m.
6.
(b) Eigenvalue is +1 ; massless particle identified with neutrino.
7.
M
(d) Ratio of rates =  K
 M
8.
(d) mq = (mn + m)/6 ; A = 2 mq2 (m - mn)/3 .
5

 tan 2  C ; (e) Ratio of rates =

48
 MK

 M
5

 tan 2  C .

F33SO2: Laser Physics and Matter-Light Interactions
1.
u = 1.5  108 ms-1 ;  = 4  105 m-1 .
2.
d = 1.6 m.
3.
Energy = 35.3 meV ;  = 7.2 ps.
4.
B = 0.31 T.
6.
 = 3.4  104 m-1 ; Max. contribution to n for  = -/2 where nmax = 4  104.
7.
Assuming materials A and B are chosen for lenses 1 and 2 respectively, then r11 = r12
= r21 = 8.6 cm. and r22 = -3.6 m.
8.
Min. pulse duration = 12  10-15 s. and repetition rate = 75 MHz.
Average power output = 2.19 W and energy per pulse = 29 nJ; E = 47.5 MV m-1.
F33SQ6: Magnetic Resonance
1.
n/N = 6.8  10-6 .
4.
(a)  = 7.3 ppm ; (c) Resonant frequency = 25.11 MHz .
6.
T1 = 721 ms ; (e) 9.29  10-9 s. and 0.67  10-9 s.
7.
(b) Eigenvalues: |1 : (-h0 - X/4) ; |2 : 0 ; |3 : X/2 ; |4 : (h0 - X/4) .
(c) E13 = h0 + 3X/4 ; E43 = h0 - 3X/4 . (d) Lines have equal intensity.
F33SS2: Solid State Physics 2
1.
vg = 0 at k = /a .
4.
Highest energy phonon mode has energy 33meV.
5.
I = 100 A.
7.
Ed = 28 meV ; radius of ground state orbit = 2 nm.
8.
vc = 26.5 ms-1 .
49
F33SV3: Atmospheric Physics and Meteorology
1.
c = - 0.2 ms-1 .
2.
0* = 0.94 .
6.
Total ozone in column = 270 D.U.
8.
Average current from cloud to ground of -0.87 A.
9.
(e) u = 1.07 ug at z = 1540 m. ; v = 0.32 ug at z = 513 m.
50