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Unformatted text preview: OM D41 1.C P
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EME Physics 102 FORM 0  PR
EME D41 1.C OM [l] In a singleslit diffraction experiment, a beam of monochromatic light passes through a
slit of width 16.0 fj,m. If the second dark fringe of the resulting diffraction p attern is at an
angle of 4.31°, what is the wavelength of the light?
[A] 301 nm
[B] 413 nm
(W)601 nm
[D] 720 nm
[E] 827 nm  PR
EME D41 1.C OM  PR
EME D41 1.C OM [2] A spy satellite is in orbit at a distance of 5.0 X 105 m above the ground. It carries a
telescope t hat can resolve the two rails of a railroad track that are 1.4 m apart using light
of wavelength 600 nm. Which one of the following statements best describes the diameter
of the lens in the telescope? ^
[A] It is less than 0.26 m.
QBj;It is greater than 0.26 m.
[C] It is less than 0.52 m.
[D] It is greater than 0.52 m.
[E] It is less t han 1.4 m.  PR
EME
D4 11. COM [3] What is the slit spacing of a diffraction grating necessary for a 600 nm light to have a
firstorder principal maximum at 25.0°?
U])1.42 fim
[B] 2.01 /zm
[C] 3.12 /xm
[D] 4.12 pm
[E] 5.44 fan.  PR
EME
D4 11. COM [4] A spaceship, traveling at O .lOOc away from a stationary enemy station, shoots a projectile
towards the station with a speed of 0.560c relative to the spaceship. What is the speed of
the projectile relative to the s tation?
[A] 0.460c
(JBj)0.487c
[C] 0.492c
[D] 0.625c
[E] 0.660c  PR
EM ED4 11. COM [5] A satellite, initially at rest in deep space, separates into two pieces which move away from
each other. Onepiece has a rest mass of 190 kg and moves away with a speed of 0.280c,
and the second piece moves in the opposite direction with a speed of 0.600c. What is the
rest mass of the second piece?
__
[A] 42.4 kg
[B] 52.7 kg
[C] 68.8 kg
(13)73.9 kg
[E] 88.7 kg  PR
EM ED4 11. COM [6] A space tow barge pushes on a spaceship with a rest mass of 15,000 kg and accelerates it
from a speed of 0.600c to a speed of 0.700c. How much work does the tow barge have to
do to accomplish this?
[A] 8.78 x 1019 J
[B] 1.35 x 1020 J
(fcfo.OS x 1020 J
[D] 2.70 x 1020 J
^^ 11. COM [E] 5.42 x 1020 J  PR
EM ED4 [7] If you approximate yourself as a blackbody emitter and you don't have a fever, what is
the peak f requency of your emission?
[B] 5.8 x 1012 Hz [C] 6.3 x 1012 Hz [D] 9.7 x 1012 Hz ED4 11. COM 2.2 x 1012 Hz
1013 Hz 11. COM  PR
EM [8] An xray photon with an energy of 1.00 X 10~15 J travels in the +x direction and is incident
on a free electron that is at rest at the origin. The photon is scattered in the — y direction.
What is the f requency of the scattered photon?
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17
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[A] 1.49 x 10 Hz
[B] 1.50 x 10 Hz
[C] 1.51 x 10 Hz
nD])l.49 x 1018 Hz PRE MED 411 .CO MPRE
M ED4 11. COM  PR
EM ED4 [E] 1.51 x 1018 Hz OM D41 1.C P
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EME Physics 102 FORM 0 1.C OM  PR
EME D41 1.C OM [9] A large collection of nonrelativistic electrons has a mean kinetic energy of 1.0 eV w ith a
corresponding spread/uncertainty in their momenta of 10%. What is the corresponding
minimum spread/uncertainty in their positions?
(OlxlO™9m
[B] 5 x 10~9 m
[C] 1 x 10~8 m
[D] 3 x 10~8 m
7
Ej 2 X 1 0~ m PRE MED 411 .CO MPRE
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EME D41 [10] The line emission in the excited gases that you observed through the d iffraction gratings
during class is due to the excited constituent atoms decaying back to their ground state.
The lifetime of these transitions is typically 10~7 seconds. Use the Heisenberg Uncertainty
Principle to compute the corresponding minimum spread/uncertainty in the energy of the
excited state. This spread in energy gives rise to the finite width of the emission line.
JAJ 5 X 10~28 eV
[B] 1 x 10~27 eV
[C] 3 x 10~27 eV
[D] 1 x 10~9 eV
9
(tip X 10 eV OM D41 1.C P
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EME D41 1.C OM [11] Two glass plates (in air) are separated by parallel fine wires, separated by a distance of
7.50 cm, as shown. The first wire, at x = 0, has a diameter ^ = 0.0400 m m, and the
second wire, at x = 7.50 cm, has a diameter d2 = 0.0415 mm. Monochromatic light of
wavelength A = 600 nm is incident from above.
(a) Consider interference between light reflected from the b ottom surface of the upper plate
and light reflected from the top surface of the lower plate, and find an expression for the
values of the separation t between these surfaces for which the interference is destructive.
(b) Find an expression for the values of x for which the interference is destructive.
(c) What is the horizontal distance (thus along the zaxis) between adjacent dark bands in
the reflected light? x [cm] 7.50  PR
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EME hysics 102 OM 1.C D41  PR
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EME D41 (Albert^ 411 .CO MPRE
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EME D41 1.C OM [12] Max and Albert are identical twins. On their 18t!l birthday, Albert takes off on an O utward
Bound spaceship expedition traveling in the zdirection at a speed of 4c/5 with respect
to Earth. Max stays on Earth and attends the University of Miami. A fter 3.0 years on
Albert's watch/calendar, Albert's Outward Bound spaceship reverses direction and heads
back to Earth on the same path at a speed of 4c/5.
(a) What is the age difference between Albert and Max once Albert returns to Earth (who is
older)?
(b) In Albert's frame of reference, his spaceship is 100 m long as measured along the xdirection. How long does Max measure the spaceship to be in the zdirection?
(c) According to Max, what f raction.of the spaceship's total relativistic energy (during its
travel) is relativistic kinetic energy? PRE £3) FORM 1 OM D41 1.C P
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EME D41 1.C OM [13] A gamma ray photon of energy E propagates in the +x direction and collides with an
identical gamma ray photon (also of energy E) traveling in the — x direction. Since parts
(b) and (c) depend on your answer for part ( a), it is suggested that you express your
answers for parts (b) and (c) in terms of E, before evaluating numerical results. This way
appropriate credit could be given on p arts (b) and (c) even if your answer for part (a) is
wrong.
(a) What is the minimum energy of each of these photons such t hat they produce a positronelectron pair? (Hint: the minimum energy results in a positron and an electron that are
at rest.)
(b) An xray with 1/100,000 the energy of the above gamma ray is incident on a gold surface
with a work f unction of 4.58 eV. What is the the maximum kinetic energy (in eV) of the
ejected photoelectron?
(c) What is the de Broglie wavelength (in m eters) of the ejected electron t hat has the maximum
kinetic energy found in part ( b)? (Hint: the ejected electron is NOT moving at relativistic
speeds, and be careful w ith units! It is suggested to express the electron energy and mass,
in the formula you use, either in Joule and kg u nits, or in eV and eV/c2 units.)  PR
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EME Physics 102  PR
EME D41 1.C OM FORMULAE SHEET me = 9.11 x 10~31^ = 0.511MeF/c2,
OM e = 1.60 x lO"19^ D41 e0 = —  PR
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fcg ,  PR
EME D41 1.C C/jg = 8.85 x lQl2C2/Nm2 4?TK OM r2 lkWh = 3.Q x 106J, 1.C leV = 1.60 x 10~19 J, k = 8.99 x WgNm2/C2 lir = ^, E = cB, COM k E = E0sin(kx uJt),  PR
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d sin^ = (m + 1 /2)A, m = 0 , l , 2 . . .
(double slit, dark)  PR
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EM ED4 11. (single slit, d ark) = 3.00 X 108rra/.s, _ 11. COM j 1 c= ED4 GO
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(double slit, grating, bright) ' F 11. U j  PR
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a n = 4?r X 10 —— » COM (thin film, L= L n \ / l — U ^ / C ^ , q  PR
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K = E  E0, D= P2
E =p2 0+pc,
E , 22 11. COM = "i0c2 , . c •Ua,. = — .
2 ED4 11. ,  PR
EM ED4 = 6.626 x 10~S4J s = 4.135 x 10~15eF s = 1 2 4 0 , H = — = 1.054 x 1 0~ 34 J s
c
2?r
= 5.88 x lO10*"1^1, ^max = hf  W0 , ^ = hf MED 411 .CO MPRE
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2m PRE A '  A = A c (lcos0), ED4 hf = hf' + K,  PR
EM p= — = ,
c
A 11. COM  2.898 x 1 0" 3 m^, , s ,
2 > 2 AC =  = 2 .426pm,
m ec
m A dB =  . T  273.15 K = Tc = (Tp  3 2°)
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 Fall '08
 Ashkenkai
 Physics, Diffraction, Light

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