Saturday, July 9, 2011
Introduction to Basic Physics (Radioactivity) - Pt. 25
We now come to the final part of the Basic Physics blog course: Radioactivity. The objective here is to get students (or interested readers) to appreciate and recognize the various types of radioactivity - in the form of their specific particles- and how these can be measured in terms of activity. Probably the last part is the most intuitive and easiest, so we begin with that: using a device called the Geiger Muller counter (shown in Fig. 1) with the general principle illustrated in Fig. 2
First, note that Fig. 2 is a simplification. In actual fact the anode is a tungsten wire with extends through the cathode, which is a metal cylinder. Both are then fitted into a gas-filled envelope which is the "Geiger-Muller" tube. A typical low pressure gas to use for the tube is Argon (Ar) which at a pressure of about 10 cm of Hg (compared to 76 cm Hg for atmospheric) easily fills the tube via diffusion. A potential difference (p.d.) of 900- 1,000 V is then applied between the anode and cathode (A and C in Fig. 2). The applied p.d. has the effect of slightly stressing the Argon in the tube so when radiation enters its ionizing action produces more ions from the gas in the tube. (In other words, the radioactive substance causes the gas atoms to lose electrons, hence be ionized).
The electric field produced (e.g. E = V/d) then accelerates these ions and many more ions are produced by way of collisions. In effect, an ionizing current is quickly built up and triggers the tube which is connected externally through an amplifier to a count-rate meter which gives the counts per minute (cpm).
Radioactivity basically occurs in three forms, as determined by the particles: alpha-radiation (from alpha particles or Helium nuclei), beta radiation, from beta particles or electrons, and gamma radiation, from gamma particles or very high energy photons (e.g. at very short wavelengths, hence can easily penetrate tissue).
The simple diagram of Fig. 3, using a simple experiment, graphically shows the differences in the radiations with respect to an applied magnetic field. If one holds the thumb of one's RIGHT hand into the image (to represent the B-field direction) then the electrons (beta particles) will display a direction coincident with the curving fingers of the right hand. That is, clockwise. Now, since the alpha particles are positively charged (, e.g. He++, as opposed to the negatively charged beta particles, e.g. e-) they will go in the opposite direction- as shown.
The gamma rays, meanwhile, suffer no deflection in the field because they have zero charge, being photons of light. In terms of penetration power these additional differences apply:
1) Alpha particles are absorbed by a few cm of air, or aluminum foil only 0.006 cm thick
2) Beta particles - while having less ionizing power than alphas (because of much lower mass) have 100 times more penetrating power. A sheet of aluminum at least 3mm thick is need to absorb them.
3) Gamma rays produce little ionization since they have no electric charge but can pass through a block of iron a foot thick.
Typical Experiment using the Geiger-Muller Tube
1. After setting the high voltage supply to minimum high voltage, bring a beta source to within about 6 inches of the G-M tube.
2. Gradually increase the voltage until the counting just starts (as disclosed by the clicking sounds from the meter). This is the "starting potential" - so record the voltage at this point. (See Fig. 4)
3. Increase the voltage to a value 100V above the starting potential - this should provide operation near the threshold (See Fig. 4)
4. Adjust the distance between the radioactive sample and the Geiger tube until the meter reads about 4,000 cpm. (Leave the sample at this distance for the balance of the plateau curve determination)
5. After returning the meter switch to the CRM position, record the count rate at the starting potential. Tne record the count rate corresponding to a series of voltages about 50 V apart.
6. When the continuous discharge region is reached immediately reduce the voltage.
7. Plot a curve on graph paper using cpm as the y-axis and voltage as the x-axis, The end result ought to be similar to that shown in Fig. 4.
Using a beta source, plot cpm as a function of distance between the source and counter. Note the extent to which the curve obtained obeys the inverse square law (i.e.g the intensity or rapidity of the count is inversely proportional to the distance of the detector from the source).
The half life of a radioactive source
Another application of the G-M tube is to find the half-life of a particular source or the activity (decay rate) - say at a place.
A Geiger-Muller tube measures the background count at a given place to be 20/min. Over a period of time, the readings below are then obtained after an unknown source is placed at the location.
Time hrs: (0) <->(6)<->(8)<->(10.5)<->(20)
Count/min: (120)--(70) -(60)--(50)--(30)
Obtain the corrected counts, determine the half -Life (T½) of the unknown source, and find the decay constant.
First, we obtain the corrected counts by subtracting the background count of 20/m from each of the values above, to obtain:
Correct/cpm: (100)--(50) -(40)--(30)--(10)
We can easily see from inspection, that since the activity drops by half (from 100 to 50 cpm) in 6 hours, that 6 hrs is the half life.
Hence:(T½) = 6 h = 21600 s
This can also be verified by sketching a plot of the half life ((T½) ) on the vertical axis against the time in hours - to obtain the radioactive decay curve.
The activity A is found from:
A = ln 2/ (T½) = 0.693/ (21600s) = 3.2 x 10^-5 /s
1) Sketch the radioactive decay curve for the practical problem and confirm that the half life is 6 hrs.
2) A point source of gamma radiation has (T½) = 30 mins. The initial count rate recorded by a G-M tube is 360/s. Find the count rate that would be recorded after 4 half lives. Sketch the decay curve and determine the activity, A.
3) At a certain instant, a sample of a radioactive material contains 10^12 atoms. The half life of the material is 30 days.
a) Calculate the no. of disintegrations in the first second.
b) The time elapsed before 10,000 atoms remain.
c) the count rate corresponding to the time in (b).
4) Find the half life of the beta particle emitting nuclide, 32P 15, if the activity A = 5.6 x 10^-7 /s.