INTRODUCTION:
If one starts with N0 nuclei at time t = 0 then the number of nuclei left after a time t is:
The rate R at which nuclei decay is therefore:
R = - N/
t
= (N0/
)e-t/
If the mean life is very long compared with the duration of an
experiment the rate R at which the nuclei decay is practically constant:
Often the life of a radioactive nucleus is expressed in terms of a ``half life"
which is the time necessary for 50% of the nuclei to decay;
= 0.69
. The above expression is an approximation valid when the time interval
t is much shorter than
, as is true in this experiment.
NOTE TO THE INSTRUCTOR: You should remove the plastic cap from the GM counter for the students studying the absorption of ![]() |
EXPERIMENT
In order to do all this fairly rapidly different groups of students will do different parts and compare their results at the end.
IMPORTANT:
When a beam of N0 particles crosses a layer of absorber of thickness t mg/cm2 the number of particles that emerge is given by:
The data has an exponential form; if one takes the logarithm of the number of particles one obtains a linear expression, which is easier to analyze:
Figure 1: Number of particles vs thickness.
Figure 2: ln N vs. thickness on log-linear paper. The slope of the line is equal to
-1/
EQUIPMENT
![]() ![]() ![]() ![]() ![]() ![]() |
PRECAUTIONS: The Geiger counter has a very thin window to permit the entry of the radiation under study; the window is protected by a plastic cap. Groups working on ![]() |
PROCEDURE I: (45 min)
Because of this the work will be divided among different
groups:
Group # 1
Poly
:
Group # 2
Pb
:
Group # 3
Al
NOTE: All Groups must make a Background measurement
These counts are mostly due to a radiation called Cosmic Rays: energetic protons and other nuclei produced somewhere in the galaxy (probably supernovæ or pulsars) that impinge on the upper reaches of the earth's atmosphere. These particles interact in the atmosphere and produce secondary particles that reach sea level, cross the roof of the laboratory and finally cross your GM tube. They are mostly electrons, positrons and muons. Their number is small
10-2/cm2 . s but not negligible. This background rate must be subtracted from all subsequent counting rate determinations for the
or
sources.
Absorber name | t | Total Counts | ![]() | N' = | ln N' |
mg/cm2 | N | = N - Nbgr | |||
Background | 0 mg/cm2 | ||||
ADDITIONAL PRECAUTIONS FOR THE BETA PARTICLES EXPERIMENT:
The absorbers for this part are extremely thin. Please treat them carefully !!!
ANALYSIS OF THE DATA