Name_______________
Mail No. _______
Test 1 (100 points)
March 2, 2012
Physics 3540
Modern Physics
INSTRUCTIONS: No references other than the constants and equations on this test paper. Points are
indicated in parentheses. GOOD LUCK!
2
e = 1.602 x 10.19 C
melectron = 9.107 X 10.31 kg = 0.511 MeV/c = 5.486 x 10-4 u
2
27
mproton=1.6726 X 10.27 kg=1.00729 u=938.271 Mev/c2
mneutron=1.6749 x 10. kg=1.00866 u=939.565 Mev/c
2
2
h = 6.626 X 10.34 J s = 4.136 X 10.15 eV s
c = 3.00 X 108 m/s
1.000 u = 1.66054 x 1O. ;l= 931.494 Mev/c
CONSTANTS:
r
~1+~c
r
EQUATlONS:Jobserved=RJsource
vx
x'=r(x-vf)
t'=r(t­
, ux -v
ux=
1-­
r(1
UXv)
l __
X_
c2
C
1
r = --;===
uy
t
uy
uv
2d sinB
n/1,
/1,'-/1,
c
=
2
- cosB)
1. (20) The average lifetime of a pi meson in its own frame of reference is 2.6 x 10.8 s. (This is the proper
lifetime.) If the meson moves with a speed of 0.90c relative to the earth, (a) (3) find y. What then is (b)
(3) its mean lifetime as measured by an observer on earth and (c) (3) the average distance it travels
before decaying, as measured by an observer on earth? (d) (3) How far is the distance of part (b) as
measured by the pi meson? (e) (6) If the pi meson has a rest mass of 139.6 Mev/c2 , determine both its
total energy and its momentum as measured on the earth.
2. (15) An electron has a kinetic energy five times greater than its rest energy.
energy. (b) (5) Find its speed. (c) (5) Find its momentum.
(a) (5) Find its total
3. (10) A spaceship moves away from Earth at a speed of 0.7c and fires a shuttle craft in the forward
direction at a speed 0.80c relative to the ship. The pilot of the shuttle craft launches a probe in the
forward direction at a speed 0.90c relative to the shuttle craft. Determine (a) (5) the speed of the shuttle
craft relative to Earth,and (b) (5) the speed of the probe relative to Earth.
4. (20) Light of wavelength 500 rim is incident on a metallic surface having a stopping potential of 0.65 V.
(a) (5) Draw a diagram, state the photoelectric equation, and briefly discuss the photoelectric effect.
(b) (5) Find the maximum kinetic energy of the emitted electrons. (c) (5) Find the work function of the
metal. (d) (5) Find the cutoff (threshold) wavelength.
5. (20) X-Rays with a wavelength of 0.04000 nm undergo Compton Scattering. (a) (7) Draw a diagram
that includes the participants in this scattering process and the angles after scattering. (b) (6) Find the
wavelength of photons scattered at an angle of 30.00 . (c) (7) Write down the conservation of energy for
your diagram of part (a) and write down an equation that would allow you to find the kinetic energy of the
scattered (recoil) electron. (You do not have to take time to do the calculation for this part.)
6. (15) Define and in some cases discuss three of the following four discussion questions: (a) (5)
Michelson-Morley Experiment and its results regarding the ether. (b) (5) Two historical attempts (which
one corresponds to the "ultraviolet catastrophe?") and one historical success to apply equations u(f,T) to
describe Blackbody Radiation.
(c) (5) How are X-Rays produced and what is X-Ray Diffraction? (d)
(5) A Minkowski (spacetime) diagram and the "spacetime interval."