Radioactivity – review of laboratory results

For presentation on May 2, 2008 by

Dr. Brian Davies, WIU Physics Dept.

Plateau voltage for Geiger tube

• We chose the plateau voltage by using a constant source and varying the voltage that was applied to the Geiger tube.

• Threshold – minimum voltage to get counts. • Plateau – approximately constant counts. • Avalanche region – get excess counts and

nonlinear behavior. • Most tubes had a plateau near 750 volts.

The applied voltage on the geiger tube collects charge due to ionizing radiation

Data for a Geiger tube, obtained 7/1/04

2300

2200

2100

2000

1900

1800

Cou

nts

per

min

ute

(cpm

)

900850800750700Geiger tube voltage (V)

Plateau for geiger tube

Data for a Geiger tube, obtained 7/1/04

2500

2000

1500

1000

500

0

Rat

e (c

pm)

900850800750700650600Geiger tube voltage (V)

Plateau for geiger tube

Inverse square law

Linear plot for inverse square law.

r

I = 1/r2

I(1) = 1

I(2) = 1/4 I(3) = 1/9

o

oo

Log-log plot for inverse square law.

• We can plot I vs. r on a log-log graph.

• We expect that I = S/4r2

• log (I) = log(S/4r2) = log(S/4) - 2 log(r)

• We expect the slope to be m = -2

• However, the detector is a volume, and parts of it are at different distance from the source, so we do not get a perfect inverse square, but usually a lower power for m.

Rate vs. distance, Co-60 source Linear plot of data obtained 7/1/04

1000

800

600

400

200

0

Rat

e (c

pm)

30252015105Distance (cm)

Co-60 source at various distances

Rate vs. distance, Co-60 source Log-log plot of data obtained 7/1/04

10

2

4

6

8100

2

4

6

81000

Rat

e (c

pm)

3 4 5 6 7 8 910

2 3

Distance (cm)

Co-60 source at various distances

Absorption of X-rays and gamma rays

• X-rays and gamma rays can be very penetrating. • Scattering of photons is not very important. It is

more probable for the photon to be absorbed by an atom in the photoelectric effect.

• The photon is absorbed with some probability as it passes through a layer of material. This results in an exponential decrease in the intensity of the radiation (in addition to the inverse square law for distance dependence).

Exponential absorption of X-rays

The exponential decrease in the intensity of the radiation due to an absorber of thickness x has this form:

I = Io exp(- x) = e - x

where Io is the intensity without the absorber,

and I is the intensity with the absorber, and

and is the linear absorption coefficient.

depends on material density and X-ray energy.

Graph of the exponential exp(-x)

exp(-x)

x

+ exp(-1) = 1/e = 0.37

exp(-0.693) = 0.5 = ½ +

exp(0) = 1+

Half-thickness for absorption of X-rays

For a particular thickness x ½ the intensity is decreased to ½ of its original magnitude. So if

I(x½) = Io exp(- x ½) = ½ Io

we solve to find the half-thickness x ½.

exp(- x ½) = ½ and x ½ = 0.693

so x ½ = 0.693 /

Calculation of half-thickness

To calculate x ½ we need to know .

As an example, for X-rays of energy 50 keV,

= 88 cm-1 (for Pb) and x ½ = 0.693/

x ½ = 0.693 / (88 cm-1) = 0.0079 cm

But for hard X-rays with energy 433 keV (Co-60),

= 2.2 cm-1 (for Pb) and we find:

x ½ = 0.693 / (2.2 cm-1) = 0.31 cm

Half-thickness data from ORTEC-online. (link)

X

X Gamma rays from Co-60

X

Rate vs. shielding thickness, Co-60 source Linear plot of data obtained 7/1/04

1200

1000

800

600

400

200

0

Rat

e (c

pm)

1.00.80.60.40.20.0Shielding thickness (cm)

Lead shielding, Co-60 source

Half-thickness is about 0.6 cm

Rate vs. shielding thickness, Co-60 source Semi-log plot of data obtained 7/1/04

5

6

7

8

9

1000

Rat

e (c

pm)

1.00.80.60.40.20.0Shielding thickness (cm)

Lead shielding, Co-60 sourceToo high due to beta?

Too high due to scattered gamma?

Range of alpha and beta particles

• The range of alpha particles is a few centimeters in air and much less in solids.

• Beta particles can travel a few meters in air or a few millimeters in organic materials.

• One cm of polymer will usually stop beta particles.

• Our experiment used high-density polyethylene, often denoted as HDPE.

Rate vs. shielding thickness, Sr-90 source Linear plot of data obtained 7/1/04

7000

6000

5000

4000

3000

2000

1000

0

Rat

e (c

pm)

1.00.80.60.40.20.0Shielding thickness (cm)

Polyethylene shielding, Sr-90 source

Rate vs. shielding thickness, Sr-90 source Semi-log plot of data obtained 7/1/04

101

102

103

104

Rat

e (c

pm)

1.00.80.60.40.20.0Shielding thickness (cm)

Polyethylene shielding, Sr-90 source