- Inverse Square Law - when is a source a point source?
- Protection by reducing exposure time - is it always valid?
- Skyshine – radiation scattering around and over shielding
Inverse Square Law - when is a source a point source?
Any radiation training course will cover the inverse square law - as applied to protection from ionising radiation. Generally the law can be stated as follows (with respect to gamma rays or x-rays):
- If you double the distance between you and a source of ionising radiation then you will quarter the dose / dose rate at the new location.
- If you half the distance between you and a source of ionising radiation, then you will have four times the dose / dose rate at the new location.
This only applies to a point source of radiation and this is not always stated as clearly as it should be.
Do I have a point source?
Consider the following diagram.
Here we have a radioactive waste drum with someone in close proximity. The rule of thumb is as follows:
The inverse square law will apply where the distance (D) from the source is at least '10*X' (where 'X' is the longest dimension of the source)
Therefore in the above diagram, regardless of the surface dose rate from the drum, its not likely it can be approximated to a point source and therefore applying the inverse square law will be unreliable. If this is a standard 200L drum then X will equal 0.85 m, and so the inverse square law might apply (at least mathematically) at distances (D) that exceed 8.5 m. However, you then need to consider the following:
- Depending on the content of drum, activity per unit volume / mass (etc), this is clearly a volume source and not a point source
- The drum contents might be 'self shielding' such that 'hot spots' measurable on the surface are not contributing in the direction of calculation (or measurement).
- Unless this is a single drum there may well be contributions from other nearby drums
- You might be too far away from the drum to detect any radiation from it
Overall all it would not be practical to treat the above case as a point source and therefore the 1/D2 inverse square relationship will not apply.
Example - when is a source is a point source?
Consider a typical high activity sealed Ir-192 source as used in industrial radiography. The radioactive Ir-192 material will be in the form of one or more small pellets (generally max dimension will be 1.5 mm). These will then be loaded into a stainless steel source capsule and welded shut. Generally the longest dimension of this capsule (the 'source') will be about 5 mm (sometimes a little more). A typical activity for this example could be 740 GBq (20 Ci).
The dose rate expected at 1 m from the source will be about 84 mSv/h (line of sight with no shielding). Clearly this is a point source since 10*D (10*5 mm) = 0.05 m and this is considerably smaller than 100 cm (1 m). We can then calculate the distance at 10 cm from the source (still a point source). We can do this as follows: [(100)2 / (10)2] * 84 mSv/h. This gives us 8400 mSv/h (we have rounded to keep numbers neat). This is a considerable dose rate.
We could go in nearer too. The dose rate at 5 cm, where the source may be about to lose its point source status, is about 34 Sv/hour (with rounding to keep numbers neat). That is around 0.5 Sv/minute.
Trying to calculate the dose rate on the surface of the source using the inverse square law will over estimate since its no longer a point source. However, this analysis shows that we can use inverse square law with such sources, and a clear message here is 'never pick up the source up with your fingers'! The dose rate to the fingers will be at least 0.5 Sv/minute, and on contact 10's times more - it will lead to radiation burns (deterministic effects).
If in doubt, and actually do this anyway, always monitor where you can and do not just rely on calculations. The inverse square law for true radiation point sources is a good planning tool to evaluate likely routine occupational exposure, and exposures arising from a radiation accident. Its also a useful training tool as it explains the advantage of modest distance increases, and highlights rapidly increasing dose rate as you move towards a radiation point source.
Protection by reducing exposure time - is it always valid?
The short answer is No! This rule of thumb is perhaps a little more abstract, but it might get you thinking. Reducing exposure by minimising time is a valid radiation safety principle in many circumstances. However, this is not always the case as these three examples will show.
Very high gamma dose rates
We will not dwell on the circumstances leading to a high dose rate, only the implication of using time as a protection measure. Consider the Co-60 activity in an industrial irradiation facility. Typical activity in such a facility might be 37 PBq (1 MCi). The dose rate at 1 m from the fully exposed sources would be in the order of 11400 Sv/h. This is therefore about 3 Sv / second. Given that the LD50-60 for survival from a high dose of ionising radiation (i.e. 50% exposed will die within 60 days without medical intervention) is about 5 Gy, then the 3 Sv / second exposure will be catastrophic. The reduction of time in these circumstances is completely irreverent - there is no thinking time to even consider protection by time. [For the purposes of this example we will assume that 1 Gy = 1 Sv whole body dose from gamma rays].
A vial containing 1 GBq of finely powered Po-210
Many years ago we did a blog article hosted on our old website which looked at the Alexander Litvinenko Po-210 event. We calculated early on in the incident that his death could have been induced by an intake of as little as 115.5 MBq (7 ug of pure Po-210). This web article is a reminder of this 2006 event (via Wikipedia) : Alexander Litvinenko ).
So consider 1 GBq of Po-210 in a sealed glass vial on an open bench. What about time protection in these circumstances? The emissions from Po-210 are a 5.3 MeV alphas with a probability of 100%, and a gamma ray of 0.8 MeV with < 0.001% probability, Essentially we say that Po-210 is an alpha emitter, but technically is also a gamma ray emitter as indicated. The gamma ray dose can be shown to be about 0.001 micro Sv/h at 1 m, and on the surface of the vial would be of the order of a few micro Sv/h at most.
Therefore, as long as the vial is intact and the Po-210 stays where it is (contained) then protection by reducing exposure time is irrelevant.
Work around an airport x-ray screening unit at departures
You queue up and wait your turn to put your cabin baggage, laptop, liquids etc into a grey tray and send it through the x-ray system. Those around the x-ray unit will include yourself (generally at the in-feed or out-feed) and other security personnel including the operator who will be located to the side of the unit looking at the display screen. The unit will contain one or more x-ray tubes typically operating at 140 kV and 1mA. Some of the latest x-ray units are based on CT (computed tomography) technology with similar kV but higher current. Whilst NOT a legal limit, the internationally recognised external instantaneous dose rate for x-ray cabinet systems will not exceed 1 micro Sv/h. Depending what you read, this will be measured at the surface, at 5 cm or 10 cm from surface. If you dig into the origin of the 1 micro Sv/h (which is based on exemption from notifying your local regulator of your use of ionising radiation), then its 10 cm from the surface. These exemptions are not always granted (they are not available in the UK for x-ray systems). However they are meant to suggest that the exposure potential is so low the the system may not need further regulatory control.
In practice most manufacturers will measure this at the surface. In the competitive world of x-ray security no company is going to supply x-ray equipment that does not meet this dose rate 'limit'. Ionactive finds that in most cases dose rates around such units are so near background that there is effectively no exposure from the x-ray unit. Sometimes we will find slightly elevated dose rates at the in-feed and out-feed, but by the time dose averaging is calculated exposure potential in these areas is no greater than background.
Therefore, operators of this type of x-ray equipment, and the security personnel near by, do not need to wear dosimetry (personal radiation monitor) and there is no restriction on working time (with respect to radiation safety). The rule of reducing exposure by minimising time does not apply.
Skyshine – radiation scattering around and over shielding
Unlike some of our other rules of thumbs, this article will take a slightly different approach by providing some insight into the issue, rather than a simple expression to calculate the effect (there are no such expressions that can be readily used to cover all source types and geometries). We will first express a simple rule of thumb and then delve into some data so you get an idea of how significant skyshine can be.
The rule of thumb: When considering radiation shielding for x-ray / gamma sources, don’t ignore radiation that might be scattering under, over or around the shielding. To do so can create quite embarrassing unexpected dose rates some distance away from the shielding!
Skyshine – visualising the problem (1)
Consider the following diagram. It depicts a radiation source of some type behind a shield (right hand side). The left-hand side represents a dose measurement point (a person). At this stage we do not need to consider height or shielding thickness, but we will assume the shielding is on firm dense ground and is infinitely wide (so we do not need to consider scattering under or around the sides of the shield, only above it).
Therefore, there are two modes for radiation to arrive at the measurement point – through the wall or over the top of the shield. Experience using real measurements has shown that it is quite possible to measure negligible dose rates close up to the shield (if the shielding provides adequate attenuation) but which increases as you move back from the shielding, reaching a peak before reducing with further increase in distance. This is Skyshine. Whilst Skyshine will be worst where there is no shielding ‘above’ the source (i.e. a radiation bunker with no top shielding), it can still be significant if only modest top shielding is use (perhaps because it is assumed no one will have access above the source).
Skyshine – visualising the problem (2)
Before looking at real sources, distances and dose rates, its often useful to try and imagine what is going on by replacing the radiation source with a very bright high intensity beam of visible light aimed downwards onto the floor. In the picture below we have a similar setup, now using a torch beam and all other sources of light are removed (any building windows are blacked out etc). Now stand right next to the wall and look at your hands. What do you see (can you see them at all?). Now move away from the wall and look around – what do you think you would ‘see’? Probably illumination from over the wall and quite possibly more of your hands. By the wall you were in a shadow, away from it you are not. Its not a perfect translation of physics between visible light and gamma / x-rays, but its good enough to visualise Skyshine.
Example – Shielding Ir-192 with a wall, analysis of skyshine potential
For this analysis we are going to make the following assumptions / decisions.
- The source is Ir-192 with an activity of 740 GBq
- The source is not collimated
- Regardless of source position, the wall will provide shielding such that the surface dose rate is < 1 micro Sv/h (calculated).
- The wall is 4m in height
- Its width is infinite (this simplifies analysis and is similar to where you have a four walled bunker)
- The wall shielding material is irrelevant
With the above accepted we can now add some dimensions to the source diagram and shown below.
We will now use the Groves MicroSkyShine code to evaluate the dose to the person (Hp) in micro Sv/h. The diagram below is a depiction of the data in MicroSkyShine, but the intention of this rules of thumb resource is not to delve into this industry standard modelling software, but rather look at the at the results.
The results are in mR/h and the results in the above table show this to be 1.99 mR/h. We have then rounded this and converted this to micro Sv/h (using 1R = 0.877 Gy in air). The result is 18 micro Sv/h.
So, let us pause…
- The source is fully shielded behind the wall, the surface dose rate is < 1 micro Sv/h on the wall (we assume this is calculated as we cannot isolate the wall dose rate from any skyshine)
- The source is low down (1m from the floor)
- The person is 2m from the wall (i.e. 3m from the inner surface of the wall) and is low down (waist height dose point taken to be 1m from the floor)
Despite the above seemingly ‘safe’ geometry, the dose rate is of the order of 18 micro Sv/h, significantly more than the < 1 micro Sv/h expected on the wall surface. That is Skyshine!
Skyshine – the effect of moving nearer to, or further from the source
Forget using the inverse square law, it will not work. Furthermore, any assumption that a ‘calculated’ shield will perform as required if the facility has an open top could lead to some embarrassment!
Using computer models can give you an inaccurate result, with perhaps MCNP (Monte Carlo) coming closest to what you might measure in reality. However, when using these models at the 'limit' (e.g. very near the shielding wall), real measurement data will be more reliable in most cases. And so for the above example, using experience of similar real life shielded sources, the dose rate on the wall surface will be substantially less than the 18 micro Sv/h measured at 2m. It will most likely tend towards <1 micro Sv/h.
Furthermore, again from experience of real-life shielding, the dose rate of 18 micro Sv/hour at 2m will be the likely maximum and this will then tend to reduced with increasing distance. This is how sky-shine can lead to unintended exposures where measurements are first taken at the wall (yielding low dose rates) and then at a significant distance away from the shield (also yielding low dose rates). You may well have missed the peak!
In the above example, moving from 2m to 4m away from the wall will reduce the dose rate to about 14 micro Sv/h. This reduction clearly shows that the inverse square law is irrelevant.
If you think you may have a sky-shine issue, or need practical advice regarding radiation shielding (particularly where you have an open top shielding bunker) then feel free to contact the Ionactive Radiation Protection Adviser (Mark Ramsay).