137
Introuction.
The half-thickness is the thickness of material required to diminish an incident beam of radiation to half its original intensity. The half-thickness is also referred to as the Half Value Layer (HVL).
When a beam of gamma rays interacts with matter, the gamma rays lose energy through the photoelectric effect, the Compton effect and pair production (with high enough energy). The intensity (I) of the beam decreases with thickness (x) according to:
I(x) = I
0 e − µ x eqn. 1
Where µ is the linear absorption coefficient. The value of µ depends on the type of matter and the gamma energy. This coefficient can also be expressed in terms of the half- thickness:
ln2 t
1
2 where t
1
2
half
thickness t
1
2
ln2
eqn. 2
Your radioactive source of gamma rays is Cs 137 . This source emits both beta and gamma rays. If you are using a GM tube (Geiger Mueller) for detection you would need to cover the source with a
scintillation detector is enclosed by aluminum that will stop the beta rays (electrons) but pass most of the gammas so you should be counting only gamma rays.
The pieces of lead (Pb) available will have thicknesses of one-eighth or one-fourth of an inch.
Procedure:
Setup. You should position the source so that you will be able to pile about ¾ of an inch of lead between the source and detector. (If the source is placed on a plastic holder and positioned in groove number four from the top, the lead can be piled on a second plastic holder in the third groove from the top.) Once you begin taking data you should not move the source relative to the detector because you want the only changes in counting gammas to be due to the lead layer.
Power the detector. Your NaI scintillation detector should be powered with 1400 volts.
Determine the background rate. You will need to subtract the always-present background radiation from your measured gamma rate. This background (counts per minute) comes from the true background and from the sources of other experimenters in the room. Move your source away from the detector so that you can determine the background radiation counts. You may do this before or after the main data gathering.

Gather the data. Record the gammas reaching the detector (counts per minute) for various lead thicknesses ranging from 0 inches to 5/8 or 6/8 inches. Conducting several trials for each lead thickness is good experimental technique – it tells you how reproducible or consistent the measurements are.
Graphs and Results.
Exponential Curve Plot.
Call I net
= I ave
–I bckgrd
. Plot I net
vs. x and draw the best smooth curve through the data points. The curve should be part of an exponential curve according to eqn. 1. Use two pairs of points read from the smooth curve to determine the half-thickness. If one point is half the intensity of the other, the difference between the x values is the half-thickness.
Straight line Plot of Natural Log.
Plot ln I net
vs x. The slope = -
µ
from which you can calculate the half-thickness using eqn. 2. If your x values are in inches, then µ has units of 1/inches and the half-thickness has units of inches.
Summary statements and questions.
State the half-thickness from each of the plots in inches and in cm.
What is the percent difference between half-thickness values using these two approaches (curved plot and straight line plot) with the same data?
Based on the value from the slope of the natural log plot, what thickness of lead is required to reduce the gamma beam intensity from a radioactive Cs 137 source to one-eighth of its initial intensity?