). Determine ( a) the change in
wavelength of the photon, ( b) the change in energy of the photon and
( c) the kinetic energy imparted to the electron.
Ph 3304 Review Problems for 1st Hour Exam October 9, 1997
Problem 1 -
a) If the work function for a metal is 1.8 eV, what would be the stopping potential for light having a wavelength of 400 nm?
b) What would be the maximum speed of the emitted photoelectrons at the metal's surface?
Answer: a) 1.3 V b) 680 km/sec.
Problem 2 - An x-ray photon of wavelength 0.01 nm strikes an
electron head on (). Determine ( a) the change in
wavelength of the photon, ( b) the change in energy of the photon and
( c) the kinetic energy imparted to the electron.
Answers: a) +4.8 pm (b) -41 keV (c) 41 keV
Problem 3 -
In 1983 the Infrared Astronomical Satellite (IRAS) detected a cloud
of solid particles surrounding the star Vega with the maximum radiated
intensity at a wavelength of 32 
m. What is the temperature
of this cloud of particles?
Answer: 91 K
Problem 4 - One cosmic-ray particle approaches the earth along its axis with a velocity of 0.80c toward the North Pole and another, with a velocity of 0.60c, toward the South Pole. What is the relative speed of approach of one particle with respect to the other?
Answer: 
Problem 5 -
A spaceship of rest length 130 m drifts past a timing station at a speed
of 
. ( a) What is the length of the spaceship as measured by
the timing station?
( b) What time interval between the passage of the front and back end of the ship will
the station monitor record?
Answer: ( a) 87.4 m ( b) 394 ns
Problem 6 - A pion is created in the higher reaches of the earth's atmosphere when an incoming high-energy cosmic-ray particle collides with an atomic nucleus. A pion so formed descends toward earth with a speed of 0.99c. In a reference frame in which they are at rest, pions decay with a mean life of 26 ns. As measured in a frame fixed with respect to the earth, how far (on the average) will such a typical pion move through the atmosphere before it decays?
Answer: 54.7 m
Problem 7 -
A spaceship is receding from the earth at a speed of 0.20c. A light
on the rear of the ship appears blue (
) to passengers
on the ship. What color would it appear to an observer on earth?
Answer: 551 nm
Problem 8 -
A 
particle with rest energy 497.7 MeV decays at rest into a
and 
each with rest energy of 139.6 MeV. Find the
kinetic energies and momenta of the 
and 
.
Answer: 
, 
Problem 9 -
A nonrelativistic particle is moving three times as fast as an
electron. The ratio of their de Broglie wavelengths, particle to
electron, is 
. By calculating its mass, identify
the particle.
Answer: a neutron (
)
Problem 10 - An ( a) proton or ( b) electron is trapped in a one-dimensional box of 100 pm in length. What is the minimum energy these particles can have?
Answer: ( a) 20.5 meV ( b) 37.7 eV
Problem 11 -
A particle is trapped in an infinite one-dimensional well of width
L. If the particle is in its ground state, evaluate the probablity
to find the particle between 
and 
.
Use the integral:
Answer: 0.6090
Problem 12 -
Find the de Broglie wavelength of ( a) a nitrogen molecule
(
) in air at room temperature (note: 
).
( b) A 5-MeV proton ( c) A 50-GeV electron ( d)
An electron moving at 
m/s.
Answers: ( a) 0.0279 nm, ( b) 13 fm, ( c) 0.025 fm, ( d) 0.73 nm