PHYSICS 252: TEST 4
4/29/15
Dr. Varriano
NAME:_________________
Do all 7 problems. The point value for each problem is indicated next to the problem number. Show all of your work in the space
provided to receive partial credit. You may use additional sheets of paper if necessary. Be sure to turn in the additional sheets with
your name written on each sheet. Put your final answer to each question on the line provided unless instructed otherwise.
A copy of relevant portions of the isotope table is attached to the test for your use.
___________________________________________________________________
1. [12 pts]
(a) How must one determine the length of a moving object if it is to be a valid measurement?
Review.
(b) Define a "proper length".
Review.
(c) Define a "proper time interval" between two events.
Review.
(d) If a particle has a relativistic mass that is three times its rest mass, how fast is it moving?
0.943c
2. [20 pts]
An electron is accelerated from rest to a speed of 0.95c in a linear accelerator. It then travels from an exit port to a metal target. The
distance from the exit port to the target is 200 cm as measured by a physicist in the lab.
(a) How much energy does it take to accelerate the electron to this speed from rest? (The rest mass of an electron is 0.511 MeV/c2.)
1.1255 MeV
(b) How many nanoseconds does it take for the electron to leave the exit port and hit the target as measured by the physicist?
7 ns
(c) Is this time interval in (b) a proper or nonproper time interval?
Nonproper
(d) What is the distance from the exit port to the target if you ask the electron?
62.5 cm
(e) Who measures the proper length from the exit port to the target, the physicist or the electron?
physicist
(f) How many nanoseconds does the trip take from the exit port to the target if you ask the electron?
2.2 ns
2
3. [14 pts]
An unstable nucleus is traveling away from you to the right at 0.75c. It suddenly decays and emits a - particle. You see the particle traveling away from you to the right at 0.60c.
(a) What size momentum do you measure for the - particle? (Express your answer in units of MeV/c.)
0.38325 MeV/c
(b) How fast is the - particle emitted with respect to the nucleus?
0.273c
(c) Is the beta particle emitted to the right or to the left from the nucleus? (Circle correct choice.)
right
left
4. [10 pts]
Uranium-232 is an isotope that has a relatively short half-life of 72 years compared to the other uranium isotopes.
(a) Find the binding energy of a U-232 nucleus.
1766 MeV
(b) What force holds this nucleus together?
Strong nuclear force
(c) Why does this nucleus have more neutrons than protons? (Answer below.)
Review.
5.[16 pts]
As indicated on the attached table, U-232 undergoes alpha and gamma decay.
(a) Write down the alpha and gamma decay equations in the space below.
Review.
(b) Is the final daughter a stable or unstable isotope?
Unstable
(c) Find the amount of energy released in the decay.
5.409 MeV
(d) If the alpha particle is ejected with 5.26 MeV of kinetic energy, then what is the energy of the emitted gamma ray?
0.149 MeV
(e) What is the wavelength of this gamma ray photon?
0.0083 nm
3
6.[14 pts]
Fill in the blanks in the following decay equations. Required element information is listed.
Review.
+
O  ______ + ______ + ______
(a) ( decay)
15
8
(b) (- decay)
32
15 P
-
(c) ( decay)
 ______ + ______ + ______
______
31
15
*
P + ______ + ______
Half-life
Z
Name
Symbol
122 secs.
7
9
Nitrogen
Fluorine
N
F
14.3 days
14
Silicon
Si
15
Phosphorus
P
16
Sulfur
S
2.62 hrs
(d) Given samples of the above radioactive isotopes with equal numbers of parent nuclei in each sample, which sample will initially
have the lowest activity? (Circle correct choice.)
(a)
(b)
(c)
7.[14 pts]
Barium-144 is used as a radioactive tracer in medical procedures because it has a short half-life. It emits - radiation and has a decay
constant of 3.492 / min. Suppose a sample of Ba-144 is sitting on a hospital shelf.
(a) Write down the decay equation for Ba-144 in the space below.
Review.
(b) About how many seconds will it take for the activity to reach half of its present value?
11.9 s
(c) If Ro is the present activity and R is the activity 60 seconds later, find the ratio R/Ro.
0.03
(d) Suppose a patient receives 25 mrems from the beta radiation and that the beta particles have an RBE factor of 1.5. How much
radiation was absorbed by the patient? (Express your answer in mrads.)
16.7 mrad
4
I have covered
up the half-life
on purpose.