Both experiments were essentially the same, move a detector away from a source of waves, and measure the intensity of the wave at certain distances, in order to determine if the intensity drops of inversely proportional to the square of the distance.
Prior to beginning the Gamma experiment using the rad count I took background counts over a period of a minute, then waited a minute, then took it again over the same time period of 1 minute. I did this at a variety of places in the lab I was using to find if there was a space with a less fluctuating background count, so my experiment would be more accurate, however I discovered the variation in the background count to be practically identical in all areas of the lab.
Gamma Experiment
The purpose of a trial experiment is not to prove the validity of a hypothesis but rather to determine which practical apparatus and working practises are best suited to the main experiment.
Practical issues
The majority of practical issues are mainly concerned with which apparatus should be used.
What must first be decided is what actual source are you going to use. We only had access to one source of Gamma radiation this was cobalt 60. So I used cobalt 60.
When dealing with the inverse square law the most obvious aspect is that you are measuring the intensity, and distance of a source, so these are the two factors which are most important.
To measure the distance of the source, I have three kinds of apparatus at my disposal, a simple metre rule, vernier scale callipers, and digital vernier scale callipers. I ruled out the sight-read vernier callipers first because of their impracticality, I feel my inexperience with them may lead to high inaccuracies, as I find it difficult to read from them.
I feel I can measure a metre rule to +- 0.5 mm, the digital vernier callipers can read to an accuracy of a hundredth of a millimetre. It is of a much higher level of accuracy, however is actually very difficult to physically use and measure small gaps without knocking the equipment and rendering the reading useless, it is easier to use over lengths of 5cms and above, but the percentage error here is so small I may as well use a ruler anyway. Also this is only a trial experiment so accuracy isn’t really that important. So I feel I will use a ruler due to its logistical benefits.
The next thing to decide is what kind of dector should be used, obviously it will be a Geiger muller counter and tube, but what kind should be used? There are two ‘Families’ of Geiger muller counter and tubes these are Scalar counters and rate meters. We only had access to two kinds of ratemeter, a large analogue Meter and a digital rad count I choose to use the digital rad count because simply it was the most recent radiation dector we had, and in previous experiments the large analogue meter had proven to be unreliable. So the digital rad count it is.
Methods
Over lengths of 15cm it is hard to ensure the point source of radiation is directed exactly at the dector, if it is not pointing directly, the error will be very small, but as distances increase the error will increase, the greater the distance the greater the error due to the angled nature of the source. To combat this I propose two things, the radiation source will be placed in a ‘L-frame’ or rig the dector will then be placed in a retort stand at an equal height to keep the source and dector at an even height. Secondly I will securely attach the meter rule to the work top I will be working on, I will ‘brace’ the rig against the ruler and then position the retort stand and clamp to be in line with the rig, which will then be left untouched, and the position of the rig in relation with the stand will be kept in place with the bracing against the straight ruler. The presence of a securely fixed ruler also helps with the actuality of taking readings. When measuring from point source to dector it is easy, if the ruler is being held in mid-air and not held against anything, to knock the equipment, or take erroneous readings. However with the ruler secured to the worktop, it not only can’t knock the equipment but makes taking measurements easy. As long as you take the first reading with the source at zero distance to the dector rather than measuring to the point source, it is now possible to use the vertical strut of the l-frame a your reference point to measurement. This makes it more accurate, and reduces the dangers of parallax.
Also what must be decided is the range of distances I will work across and the increments by which I will increase my distance. I feel the best distance to measure across will be from zero distance, through to 15 cms. And I also feel it is advisable to increase in stages of 5mm. I believe if we plot distance against 1/√c then a straight line will be described, so a sufficient number of results are necessary to accurately plot this.
Light experiment
Practical issues
The practical issues at hand here, are far less complicated than that of the Gamma radiation experiment. We have a limited amount of resources available.
I could have constructed an LDR circuit attached to a ohm meter, this would gage the changing resistance of the circuit as the light source is moved away. However this is impractical, and although would prove an inverses square relationship it doesn’t deal in the basic units. In order to get a direct reading of the changing lux readings it would be sensible to use a light sensor and a large analogue meter meter. I will use a Griffin and George ray box with 12v bulb as the source of light. The only real decision to be made here is what form of measurement device is to be used to measure the distance of the source for the dector. I have decided to measure roughly over 25 cm, this means I simply cannot use either the digital, or sight-read vernier callipers, as they have a range only up to 15 cm. So I must use a metre rule.
Methods
The experiment is very similar to the Gamma experiment, in that you are moving a point source away from a dector at steady intervals. The only complex detail was ensure the ray of light pointed directly at the centre of the dector, which can be done simply by sight, by looking at it and ensuring that it is pointing at the centre.
The dector will be held in a clamp at the level of the filament lamp, and again a metre rule will be taped to the desk, in which the light box will be ‘braced’ against, I will then move it way from the dector in intervals of 1 cm over a range of 25 cm, no repeats are needed, not because accuracy isn’t essential but the wave is fundamentally different. With the gamma we had to wait for it to decay, light however does not decay it emits a constant stream of photons, so the level of light intensity will be the same from one second to the next.
What is essential is to take a ‘background count’ of ambient light; simply leaving the light dector will do this.
(See appendix for results and graph of trial experiments.)
Conclusion of trial experiments
My trial experiments have helped define which of the electromagnetic waves I will investigate closer in the main experiment. I have chosen to further investigate the area of the electromagnetic spectrum with wavelengths starching from 10-10 m to 10-13 m, better known as Gamma radiation.
My experimental results for light were much better than those of Gamma, and this is precisely why I want to further investigate Gamma radiation. I have already proved that the inverse square law holds for Light radiation, this is shown on the graph in which I plotted distance against intensity in Lux’s. It proved a curve, with a constant half-life. This shows that when the distance is doubled, the intensity halves. So I have already proved the inverse square law is correct for light, so there is nothing else to do.
I feel my relatively poor results with Gamma radiation are not due to poor experimental techniques, or that it simply doesn’t obey the inverse square law, but due to the weakness of the Gamma radiation source. As you see on the graph of distance against the reciprocal of the square root of the count, it is a straight line up to a distance of about 40mm then it ceases to show a correlation. If you look at my table of results you will see that at around the distance of 40mm the radiation count drops to a level almost equal to that of the background count. So any results after this point are not reliable.
So in order to prove that Gamma radiation, and all members of the electromagnetic spectrum, obey the inverse square law I will merely have to work over a distance up to, but not beyond about 30mm. This will mean having to take readings with smaller distances in-between so will facilitate the need for the usage of the digital vernier scale callipers, as they have a higher level of accuracy.
Apparatus
Meter rule
Digital Vernier scale callipers
Cobalt 60
Tweezers
Source rig
Retort stand and clamp
Digital Geiger-Muller counter and tube
Stopwatch
Safety
In reference to the safety aspect, the radiation source is kept inside a lead block, inside a wooden box, inside another wooden block, tongues are present for the movement of the source so it never directly handled. The sources themselves are in holders, which channel the radioactive output in one direction alone. However as I am working with Gamma radiation this is slightly irrelevant.
Also the rad-count dector will be placed in a clamp, to ensure it’s constant position. The radiation source itself is placed in a L-frame; this will keep it at a constant height. It also reduces the amount of handling needed of the sample. I also made sure that I was over 16 years of age before beginning, and made a concerted effort not to ingest the radiation source.
Method
- Take the background count of radiation by turning on the digital radcount, and setting to detection for 1 minute three times.
- Remove the cobalt-60 from its lead container, and using tweezers put in the l-frame source rig.
- Securely attach a metre rule to the desk, brace the l-frame against it, with the vertical section corresponding to a whole number on the metre rule
- Secure the digital rad-count dector in a clamp attached to a retort stand, align this with the cobalt-60 and place it to be touching.
- Set the digital rad-count to detection, for one minute, do this three times
- Move the l-frame what you estimate to be 2.5 mm from the digital rad-count, and set the digital vernier callipers to 2.5 mm, cheek the distance of the l-frame and refine as necessary.
- Repeat steps five and six until a distance of 3cm is achieved. Repeat step 1 at distance 1.5 cm and 3cm.
Analysis of Results
I feel that my results prove that gamma radiation does obey the inverse square law; to begin with we will look at the graph in which the radiation count is plotted against distance
A curve is described thus suggesting that intensity is inversely proportional to the distance. However this graph goes no way to prove that it is inversely proportional to the square of the distance, for that we need to construct a graph with one over the square root of the radiation count plotted against distance. My graph clearly shows a straight line. Thus it is shown that Gamma radiation obeys the inverse square law.
By saying that the intensity of a source will decrease inversely proportional to the square of the distance we are saying that when distance is plotted on the x axis of a graph, and intensity on the y axis we are saying that y is proportional to 1 over x squared or,
Y ∞ 1
X2
However this can be re-arranged to state that,
Y∞ X-2
If we take Logarithms of both sides of the equation we see that,
LOG Y ∞ LOG X-2
With further rearrangement we obtain the equation,
LOG Y ∞ -2 x LOG X
So by taking the LOG X function to the other side of the equation we are left with an equation of the form,
LOG Y/ LOG X ∞ -2
In other words if the data does exhibit a inverse square relationship, when a logarithm graph of the x and y values are taken, the gradient should be minus two.
Therefore if the equation of the line described on the Logarithm graph is of the form
Y = -2X + C
Then the inverse square law is proved.
However the Equation I achieve is actually Y= -0.77X + 3.02, but rather than proving that gamma radiation doesn’t obey the inverse square law, I feel it merely points out certain experimental errors, namely the inaccuracies in distance. Although they may only have been +- 0.5 mm, when working on a scale of 2.5 mm at times the percentage error is very high.
So I feel that these graphs more than adequately prove the inverse square law holds for gamma radiation.
My trial experiment in light also proves that the inverse square law holds for light.
In a similar method to the gamma experiment if we plot a graph of light intensity against distance, we obtain a curve. The fact it is a curve is good, however it is more than that it is a curve, with an almost perfect half life, the value not changing significantly for each half-life. Being around 2.5cm. The fact it has such a good half-life makes the need for further graphs redundant, it conclusively proves the inverse square law. The half-life shows that if the distance is doubled the intensity is decreased by a factor of four.
The fact that light and gamma radiation obey the inverse square law is solid proof that all members of the electromagnetic spectrum will obey the inverse square law.
Evaluation
Systematic Errors
There was a high uncertainty in my measurement of distance. The cobalt 60 is kept within a metal tube. During my experimental procedure, I measured from the front of this tube, however the source could have been up to 5mm into the tube. Over short distances this leads to very high percentage errors. A similar thing is present in the Geiger-muller counter and tube. Like previously the actual dector is set inside the plastic casing, and could have been up to 5mm inside the tube. This leads to very high percentage errors again, which I will calculate later.
There is a possibility that the counter and radiation source were actually slightly out of line, so as the two moved apart, there would be a horizontal angular discrepancy, this would lead to a count lower than it should be. However, attaching a meter rule to the desktop and bracing both the source clamp and the retort stand against it, and ensuring the two align as closely as possible, this problem is solved, this should also solve the problem on the vertical angular discrepancy. More extreme measures include bracing the equipment against the secure ruler to eliminate horizontal angular discrepancies, and attaching mini spirit levels to the source and detector to ensure the vertical angular discrepancies are kept to a minimum. It could also be possible to attach a laser pen to one of the pieces of equipment and ensuring the position of the laser light on the opposing piece of equipment doesn’t change. This will eliminate both horizontal and vertical angular discrepancies.
However these tow suggestions are impractical, the only laser light I have access to is actually very powerful, and could easily blind if directed at the ye, so I feel the danger levels here are to high. I only have access to large sprit levels, which would not be practical to attach to the equipment. Plus as I am only working over small distances any angular discrepancy will not produce high percentage errors.
Another possible error would be if the count exceeds the level at which the dector could perceive. This would lead to what is known as ‘dead time.’ As there is radioactive activity not being detected hence a deceptively low count would be present. But for this to occur it would require radiation counts far in excess of what the weak Gamma source I used was capable of, so this can be ignored.
Random errors
Working with radiation gives random errors a high significance. This is because the background count of radiation is completely random, and is subject to fluctuations. However it is not only the background that is both random, and fluctuating (randomly random) but it is the radiation source itself will have an element of unpredictability, as that there is no guarantee that it is going to decay at a constant level, in all directions. However these can both be overcome. By taking readings of the background count over 3 one-minute periods, and taking an aggregated value reduces the fluctuating nature of the background count. However we can still not have a completely accurate measure of background radiation, as a value taken before the beginning of what is quite a lengthy experiment is not necessarily the same as what the count will be half way through the experiment or after, so I took a background count before the beginning of the experiment and half-way through to ensure less errors.
To overcome the uncertainty in the radiation source itself, for each distance I intended to take 3 one minute long readings. However I did not do this blindly, if the first two were almost Identical I didn’t bother with a third, conversely if I had three very different answers, I would take a fourth measurement of the count again over 1 minute.
One other area of my experimental procedure, which could have harboured random errors, would have been any parallax in my reading of distances. However I feel I kept this to a minimum as I ensured I kept level, and in the same plane of my measurement device.
Percentage Errors
In order to gauge where the largest errors occurred in order to know which areas are to be improved were the experiment to be done again, I have decided to put a percentage value to any experimental errors.
The timing of the experiment was done with a stop watch over a one minute period, I will assume that the watch ran correctly, the accepted human reaction time is around 0.8 seconds, so I feel my measurement of time would have been accurate to +- 0.8 seconds over a 60 second period this gives a percentage error of;
0.8 = 0.0133
60
To gain a percentage error we will now times this by a hundred,
0.0133 X 100 = 1.3%
So the error due to time is 1.3%, however over shorter time periods the factor of plus or minus 0.8 seconds would become much more relevant. In future to decrease the percentage error of this plus or minus 0.8 seconds it would be possible to increase the time period, if the time period was to be doubled the percentage error would half to 0.6%. So in future rather than taking three separate 1 minute readings I would take a single three minute reading so this would decrease the 1.3% error to only a 0.43% error. They may only be small percentage errors, but when the radiation count is low that period of time uncertainty becomes important as it may harbour unknown radiation counts.
It is impossible to put a value to the uncertainty in the background count and the fluctuating decay of the radiation source, as by definition these are random and spontaneous.
So this leaves only the errors in the measurement of distance. I feel that I maintained an accuracy of +-0.5mm. So over the longer distances of around 2cm it has percentage error of about,
0.5 = 0.02 X 100 = 2%
25
However over shorter distances the errors relevance increases, for instance over a distance of 5 mm the percentage error is,
0.5 = 0.1 X 100 = 10%
5
This is quite high and must be addressed. The problem arises from the short distances I am working across. This is because the count due to the radiation source soon drops to being similar to that of the background count, and when over your count is made up of a randomly fluctuating background radiation any result cannot be trusted. So it would be possible to increase the accuracy of measurement. For instance it may be possible to set the experiment up on a travelling telescope, which will enable easier and more accurate readings of distance.
But what would be a lot easier would be to work with a more powerful source of Gamma radiation, this means it would be possible to work over longer distances, meaning the shorter, more unreliable distances have less significance placed on them.
The availability of only one source of Gamma radiation was the most limiting factor in this experiment.
However the distance inaccuracy eclipsed by, as earlier mentioned, the positions of the actual radiation source and dector within their respective tubes have an uncertainty. It is possible to estimate a value foe the combined distances. If you extrapolate the straight line on the graph in which distance is plotted against the reciprocal you will see that it crosses the x-axis at around 20mm. Dividing the y-axis intercept by the gradient, to gain a value of when the x-axis is crossed, does this.
0.0493 = 20.44
0.0024
This can be considered to be an estimation of the combined erroneous distance of the source and tube.
Over my first distance of 2.5 mm this would lead to a percentage error of,
20 = 8 X 100 = 800%
2.5
This is obviously an unacceptable level of error, however is not as bad as it sounds as it is a systematic error so will affect each result the same amount, so relative to each other the results will not be perverse. The only difference it will make will be to the gradient of a line. I feel that it is responsible for the fact that in my logarithm graph the gradient is -0.86 rather than 2. The other people doing the same experiment also got a gradient of around –0.8 so I feel my reasoning here is justified.
But this is the glaring error, and should I do the experiment I would either try to have direct measurement from actual source to actual dector to eliminate this error. Or find out the value of the error and add it to the measured distance, in a similar way we work out the background radiation count, and then subtract it from our radiation count.
In conclusion it is hard to give an overall percentage error in my result. This is because as the distance of the source from the dector changes, so does the relevance of the error. As distance increases any inaccuracy in measurement decreases. However I will give a total percentage error at the distance of 10mm.
Error of measurement +- 0.5mm – +- 5%
Error due to timing +- 0.8 seconds – +-1.3%
Error due to unknown position of source and dector 20mm – 200%
So the total error would be 206.3%
However I will choose to ignore the last one, because unlike the others it is not plus or minus, it is constant at present in all results so the final percentage error is;
+- 6.3%
In conclusion I feel I have proved that both gamma and Light radiation Obey the inverse square law, I feel this is sufficient data to say that all members of the electro-magnetic spectrum obey the inverse square law.