GEIGER-MULLER COUNTER (I)
Introduction
A typical G.M. tube consists essentially of a cylindrical cathode in the form of a graphite coating on the inner wall of a glass envelope and an anode in the form of fine tungsten wire which stretches within and along the axis of the tube. Usually it is filled with a mixture of an inert gas (argon or neon) at a partial pressure of about 100 torr and a quenching gas (halogens or organic vapours) at about 10 torr. To allow 1onis1ng particles to enter the tube, a window covered with a thin sheet of mica is provided at one end of a tube.
In operation, a sufficiently large potential difference i.e. applied across the anode and cathode of the tube so that a high radial electric field near the central wire is obtained. Under this condition, electrons produced by ionizing collisions between a high-speed particle entering the tube and the inert gas atoms are accelerated towards the anode wire by the strong electric field and acquire within a very short distance a high speed of their own. Because of this speed, they too can ionize other atoms and free more electrons. This multiplication of charges repeats itself in rapid succession producing within a very short interval of time an avalanche of electrons.
The electron avalanche is concentrated near the central wire while the positive ions, being much heavier, drift slowly toward the cathode. For a G.M. tube with a cathode of radius 1cm, the time of flight of the positive ions is roughly about 100 microseconds, which is about 100 times longer than the time necessary to build up the electron avalanche. The consequence of this is that after the initiation of an electron avalanche by an entering particle the slowly moving positive ion sheath around the anode wire increases the effective radius of the anodes. The electric field round the wire therefore drops to a value below that which is capable of supporting ionization by collision. The electron avalanche ceases and a pulse of current due to this avalanche is subsequently produced.
The object of the counter is to produce a single pulse for each particle entering the tube. This can only be achieved if spurious pulses due to secondary electrons released from the cathode surface by the bombardment of ions are completely suppressed so that the tube can recover as quickly as possible to be in a state when it is able to record the next entering particle. A quenching gas (it must be both polyatomic and of low ionization potential) introduced into the tube is to serve this purpose. The idea is to allow the inert gas ions on their way to the cathode to collide with the heavy molecules thereby transfer their charges to the molecules and become neutralized - a process known as quenching. The molecular ions thus produced move slowly to the cathode and on reaching there, capture electrons from the cathode surface to become neutral molecules. Any excess energy that the neutral molecules have will cause them to dissociate into individual atoms rather than be imparted to the cathode to produce fresh electrons that would take part in further ionizing collisions.
The usual G.M. counter circuit is as shown in the following block diagram:
where R, a register of several , is connected in series with the stabilized H.T. supply and the tube. The current pulse initiated in the tube by an entering particle produces a voltage pulse across this resistor. The output pulse is then fed via a capacitor C to a pulse amplifier, which is followed by an electronic scaling unit for recording the number of pulses. The register is usually composed of decade counting tubes. Sometimes, in additional to decade counting tubes, mechanical registers are also used.
Typically, the counting rate of a G.M. counter depends on the applied voltage. Below a minimum voltage, the threshold voltage, no counts will be registered. This minimum voltage is a function of the gas pressure and the anode diameter, and may be between 300V and 900V. As the voltage is increased, more and more counts are registered. Over a range of voltages, called the plateau range, the counting rate is relatively insensitive to applied voltage. The change in counting rate over a 100V range of applied voltage may be as little as 5V. Organic quenched tubes usually have a flatter plateau than halogen quenched tubes. For still higher applied voltages the tube may go into continuous discharge. It is particularly important that an organic-quenched tube not be permitted to go into continuous discharge, as the quenching gas may be exhausted in this way.
In this experiment a counter, which incorporates all the decade necessary components, described above in one single unit is provided. The G. M. tube connected to the decade counter is of type Mullard MX168. It has a mica window and uses halogens as quenching gas.
Students are advised to do additional reading and answer the following questions:
(i) Would the counter perform its normal duty if the polarities of the central wire and the inner wall of the tube were interchanged?
(ii) Is there any advantage of using halogens rather than organic vapours as quenching gases? Explain.
Experiment
(a) G.M. Tube Characteristics
Using handling forceps, place the radium source on the lowest shelf of the lead castle directly below the window of the G.M. tube. Switch on the counter and allow it to warm up for a couple of minutes. Increase the applied voltage from 320V in steps of 10V up to 450V. At each setting, note down the number of counts over a period of 2 minutes.
Plot a graph of count rate per minute against the applied voltage. Indicate on your graph the plateau, the Geiger threshold voltage and the operating voltage (i.e. the voltage at the middle of the plateau).
(b) Background Count
Remove all radioactive sources from the vicinity of the G.M. tube. Set the counter voltage at the operating voltage and take a 5-minute background count.
Note: The background count rate per minute should be subtracted from all counts in subsequent experiments in order to obtain the true count rates due to radioactive sources alone.
(c) The Resolution Time of a G.M. Counter
After a pulse is registered, a sheath of positive ions that gradually increases in radius remains about the anode wire. This effectively decreases the potential gradient near the wire and not until this space charge has drifted sufficiently far from the anode will the counter become sensitive again. The total time taken for the tube to recover to its fully sensitive state to give the next pulse, is called the resolution time.
For a tube having a resolution time t, it means that for each single count registered. The tube is inoperative for t sec. Thus if we have n record sounds registered per sec., the lost time in one sec is nt and the effective operating time is sec. Following from this, if we assume that the corrected count rate is N counts per sec. Then
The resolution time can be found readily using the "two-source" method. This is carried out experimentally by counting the two sources one at a time and then both together. If are the counts registered per minute for the first source, the second source and the combination of the two sources respectively, we can write:
and
Since
which follows
From , we have
Substituting into , we obtain after manipulating:
Normally , we can approximate to
which yields
Using forceps, place a radium source left of center on the bottom shelf of the lead castle. Then add another radium source symmetrically to the right of center on the same shaft and finally remove the first source without disturbing the second source. At each of these stages make a two-minute count. Correct all the observed counts for background and calculate the resolution time of the counter.
(d) Verification of Inverse Square Law
Remove the G.M. tube from the lead castle and attach it horizontally to a stand provided. Using forceps, a place a radium source on another stand and align it until its active face faces the tube window and lies along the axis of the tube. Starting with a separation d between the window and the source equal to 10cm and thereafter increase d successively by 10cm until it reaches 70cm, note down the number of counts per minute at each setting.
Correct the observed counts for background and resolution time using equation (1), and hence plot the corrected count rate against to verify the inverse square law.
Repeat the above experiment with in place of the . On the same graph paper, give a plot of the inverse-square law for the and hence from the gradients of the two linear plots deduce the strength of .
(e) Attenuation of by Matter
The attenuation of a beam of passing through matter depends on photoelectric absorption, Compton scattering and pail production. The relative importance of each of these processes, in any given case, is a function of the initial energy of the -photons and the atomic weight of the absorbing material. Experimentally it has been found that the attenuation follows closely the exponential law i.e. I is the initial intensity of the , then after transversing a layer of matter of thickness , its intensity I is reduced to
where is known as the linear absorption coefficient of the matter. The value of when the initial intensity is reduced to half is called the half value layer (HVL).
Note that in experiments using a G.M. counter, I is proportional to N (the counting rate corrected for background and resolution time), hence
Place the at a distance of about 20cm from the window of the G.M. tube. Take a one-minute count to determine the initial count rate. Without disturbing the setup, take a series of one-minute counts as a succession of aluminum sheets is placed vertically in the region between the G.M. tube and the source using the data obtained, plot a suitable graph and hence deduce the and HVL for .
References
(1) J.B.A. England, Techniques in Nuclear Structure Physics,
Part 1, Chapter 1.
(2) W.E. Burcham, Nuclear Physics An Introduction,
Second Edition, Chapter 6.
1