- Distance travelled by Alpha Particles in air and other materials
- Distance travelled by Beta Particles in air and other materials
- Formula for calculating dose rates from gamma emitting radioactive materials
- The 10 half-life rule of thumb for radioactive materials

## Distance travelled by Alpha Particles in air and other materials

#### The rule of thumb

**A rule of thumb for alpha particles in real world radiation safety is that they travel 1-3 cm in air, and their penetration through other material is negligible. They are inherently more difficult to monitor for in the workplace when compared to beta, gamma and x-ray radiations**.

**An alpha particle would need an energy of at least 7.5 MeV in order to penetrate the protective (dead) layer of skin, which is taken to be 0.07 mm**.

#### Some further thoughts on the alpha particle

In real world workplace situations, the rules of thumb given above are valid when you know the nature of the source. They are valid where you have a bonded / fixed source (one where the alpha material is not mobile). Where the source material is mobile (e.g. powdered Po-210) there is an entirely different and potentially significant internal radiation hazard. However, this is not for consideration in this section since the movement of radioactive material in the environment is very different from the ‘movement’ of the radiation particle being emitted.

Where radioactive materials emit more than just alpha particles (e.g. Am-241) they create additional external hazards from beta or gamma radiation. In the case of Am-241, except when using as an alpha monitor check source, alpha particles are irrelevant as the radioactive material will be fully encapsulated in stainless steel with a thin foil window. In this example it is the 60 keV gamma rays that are of use (e.g. for liquid fill level gauges in bottling plants).

Consider a 5 GBq encapsulated source of Am-241 (typical activity of a radiometric fill level gauge). If this source is not shielded then the photon (gamma and x-ray) dose rate would be about 20 micro Sv/h at 1 m. Assuming the source is in the gauge, and a radiation beam interacts with a test subject at 10 cm through a collimator, then the dose rate is likely to be up to 200 micro Sv/h (based on actual measurement and not the inverse square law). Now imagine your hand is 2 cm from the source where its unshielded, not collimated and not encapsulated, then the photon dose rate will be of the order of 5000 micro Sv/h. Your radiation exposure from alpha particles will be zero, even though some of them will be reaching your fingers.

#### What is the range of the alpha particle in air?

**Am-241** has 25 possible alpha particle emissions, each with a different energy and probability of emission. The 5485 keV alpha (emission probability 85%) has a mean range in air (at standard temperature and pressure) of **4 cm** (some will travel further but with a rapidly reducing intensity).

**Po-210** has two possible alpha particle emissions, the most probable being 5304 keV (100%), and the mean distance travelled in air will be about **3.5 cm**.

Some obscure or more exotic radioactive materials have much higher alpha particle emission energy. For example, **Po-212** has an alpha particle emission of over 10 MeV with a mean range in air of **10.5 cm** (half life of Po-212 is 45 seconds).

#### Practical issues monitoring for alpha emitting radioactive material

The distances travelled by alpha particles in air are based on measurements made in ideal conditions (i.e. experimentally). Workplace measurements (made by Ionactive and others) show that real world distances are much less, to a point where such direct monitoring is impracticable in some circumstances. Practical issues that will affect alpha particle monitoring include:

- The physical nature of the material emitting the alpha particles (dust, sludge, particulate)
- The type of surface the alpha emitting material is on (smooth, rough, pitted etc)
- Environmental factors (e.g. surface might be wet, or changing orientation)
- Type of monitoring probe (GM, scintillation)
- Probe window thickness, (protective) mesh spacing and shape, and overall detection area
- The skill of the monitoring surveyor (very important!)
- Other surface features (sharp edges, nails, screws) that could damage probe if too near the surface

Monitoring clothing for pure alpha emitters is particularly difficult due to the potential for folds and uneven surfaces (fabric dependent).

Here is a T201 alpha / beta monitor based on GM tube technology. The probe area is quite small so not ideal for larger surfaces, but can be useful when monitoring in confined spaces (e.g. inside ducting).

## Distance travelled by Beta Particles in air and other materials

#### The rule of thumbs

**The distance a beta particle will travel in air (its range) is given by: Range _{air} = 3.7 m per MeV**

The E_{max} for P-32 is 1.71 MeV. Therefore the maximum range in air with no other shielding medium would be 6.3 m. This might come as a surprise, but it should be noted this is E_{max}, so its the absolute maximum range of a P-32 beta particles (the intensity of beta particles will be much less than at the average distance).

**The average energy of a beta particle can be expressed as E _{ave} (beta) = 1/3 E_{max} (beta)**

Therefore, the E_{ave} (beta) for P-32 should be about 0.57 MeV (its actually 0.695 MeV from resource tables). Its a reasonable approximation to show that the average distance (peak number of beta particles) is more like 2.1 m (average energy approximation) or 2.57 m (for known average beta energy).

So far we have only considered the distance that beta particles will travel through air. In order to provide a rules of thumb to cover all other materials it is advantageous to consider distance (range) in terms of the g/cm^{2} or (mg/cm^{2}). Where the range is given in g/cm^{2}, the linear thickness of a particular material can then be determined by division of the materials density (in g/cm^{3}). A very simple relationship is then as follows.

**The range (R) of beta particles in matter rules of thumb is given by R (g/cm ^{2}) = E_{max} / 2**

The density of air at standard temperature and pressure is 0.001225 g/cm³. Using this expression for P-32 (beta max energy is 1.7 MeV), we find that R (g/cm^{2}) = 1.7/2 = 0.85. We can then covert this to distance by dividing by the density of air. Therefore 0.85 g/cm^{2} / 0.001225 g/cm³ = 693 cm = 6.9 m. Whilst not exactly the same, this compares well with the 6.3 m calculated above using Range_{air} = 3.7 m per MeV. This simple rules of thumb is reliable enough for workplace radiation safety where E_{max} is in the range of 1-4 MeV.

If you would like to use a more sophisticated rules of thumb for beta distance in any particular material then you need to use expressions based on curve fitting of beta max energy (MeV) against range (distance) in mg/cm³. More than one rule is required in order to provide a best 'fit' for each part of the curve.

**The range (R) of beta particles in matter rules of thumb (from curve fitting) are given by R(mg/cm ^{2}) as follows:**

(0.01 ≥ E ≥ 2.5 MeV)

(where E > 2.5 MeV)

The value of **E** in the above expressions represents** E _{max}** (maximum beta particle energy in MeV).

The distance beta particles travel in materials - discussion

Using the curve fitting rules of thumb we can compare range in air with similar expressions given previously. Using P-32 we can calculate the range based on an E_{max} of 1.71 MeV. The equation for this will look like the following:

The calculation shows that R = 790 mg/cm^{2}.

The density of air is 1.225 mg/cm³ and therefore the maximum range of P-32 beta particles in air is shown to be 645 cm (6.45 m) by dividing the value calculated for R by the density of air.

This result is pretty close to the values calculated above, being nearly identical to the 'Range_{air} = 3.7 m per MeV' rule of thumb (which was 6.3 m).

If we perform the same calculation for C-14 (E_{max} of 0.156 MeV), we will find that the maximum distance in air is 23 cm.

#### Using the beta range rule of thumb to demonstrate beta shielding performance

It is often said that **10 mm of perspex**, Poly(methyl methacrylate), is ideal for protection against beta radiation from common beta emitters found in the workplace. The choice of perspex serves three main purposes:

- The perspex offers a near 100% reduction in beta radiation (i.e. near enough 100% shielding)
- The use of low density shielding reduces the production of bremsstrahlung (x-ray) radiation (see rules of thumb on beta bremsstrahlung)
- The use of a transparent shield, particularly in laboratory situations, provides clear viability when working with beta emitters

A common high energy beta emitter used in the workplace is P-32 as already featured above. We can use the above equation to investigate the P-32 beta range in perspex and see if the 10 mm thickness is justified.

The value of R, for P-32, was shown to be 790 mg/cm^{2}. The density of perspex is 1180 mg/cm^{3}. Recall that we need to take the value of R, and divide by the density of perspex which gives us 0.7 cm (7 mm). Therefore, 10 mm of perspex seems a safe bet.

Now consider much higher energy beta emitter, Sr-90. The beta emission from Sr-90 is only 0.54 MeV, however its daughter is Y-90 and this has a beta max of 2.27 MeV. Therefore we need to protect against the Y-90 beta emission when using Sr-90.

Using the above equation, we see for Sr-90 (Y-90) that the value of R = 1090 mg/cm^{2}.

Noting the density of perspex is 1180 mg/cm^{3},_{} and dividing into the value of R, we see that the thickness should be 0.92 cm (9.2 mm). Therefore even for higher energy beta emitters, 10 mm of perspex should provide 100% beta attenuation with minimal bremsstrahlung. [Bremsstrahlung from beta particle interaction with matter will be demonstrated in a separate rules of thumb article].

## Formula for calculating dose rates from gamma emitting radioactive materials

There are a number of formulae available for calculating gamma dose rates from radioactive material. Since the internet now has so much data available online, using a formula is probably consigned to academic interest. As long as you know the data is reliable (and seek Radiation Protection Adviser advice if required), then you will probably find using specific gamma ray constants of more use. Just try googling 'gamma ray constant Cs-137' and you will see what we mean! That said, you need to be really careful what you choose to use, you will sometimes find quite different values if you search for them.

Doing such a search for **Cs-137** revealed the following results (we have converted all to SI units and scaled so they are directly comparable).

- 1156 micro Sv/h per GBq at 30 cm (
*search result 1*) - 848 micro Sv/h per GBq at 30 cm (
*search result 2, online calculator*) - 1146 micro Sv/h per GBq at 30 cm (
*search result 3*)

Why the difference? Part of the difference is down to the derivation of the gamma ray constant and the dose unit it is quoted in. For example, do you have the exposure in air (e.g. micro Gy/hour) or exposure in tissue (micro Sv/h). Moreover, do you actually know the unit quoted (and is it correct)?

There is a temptation (and we did this above to make the point) to convert units without thinking too hard what they actually mean.

In the first example above. according to the web page we landed on, our first result should actually read 1156 micro Gy/ h (this being derived from the data which was actually reported as 115.6 mR/hour (the R being the roentgen!). Without more thought (actually this was deliberate) we just multiplied mR by 10 and settled on the units of micro Sv/h. Is is this wrong? Does it matter? The answer is 'is depends'. If you wish to consider this further then check out the '* Additional thoughts on this rule of thumb' at the bottom of the page*'.

#### A simple rule of thumb

Here is the rule of thumb formula, it is something Mark Ramsay came across at the beginning of his career in radiation protection. It was in the book 'Introduction to Radiation Protection' by Alan Martin and was probably read about 1986.

In this expression

D = Dose rate in (micro Sv/h)

M = Activity in MBq

E = Gamma energy in MeV

r = distance from the source in m

The deceptively simple factor '6' actually ties up a load of variables converting activity (Bq) to disintegrations per second, eV to joules, joules per kg to Gy, Gy to Sv, seconds to hours, and accounting for an average (μ_{en}/ρ)_{air } which is the mass energy absorption coefficient for air, and so on. The end result is an equation that works for the energy range of about 0.1 MeV up to 2 MeV (in most cases, but see below). The best way to think of D (micro Sv/h) is what you might expect to measure from an unshielded source using a typical workplace radiation monitor.

#### Using this rule of thumb with Cs-137

Let us use the equation with **Cs-137** since its gamma emission (from the decay product Ba-137m) is simple (one gamma ray line of interest).

D = Dose rate in (micro Sv/h) - **this is what we want**

M = Activity in MBq (1000 MBq ,since we want 1GBq to match the search results we obtained earlier)

E = Gamma energy in MeV (0.662 MeV, obtained from any data book)

r = distance from the source in m (0.3 m to match the search results we obtained above).

We see that D = **1226 micro Sv/h**. A little higher than the above search results, but pretty close. (If you are not satisfied with 'pretty close' then do please read to the bottom of this page).

Before concluding we should also consider a case where the radioactive material of choice emits more than one specific gamma ray energy. In fact, we need to know the energy lines and their emission probability.

#### Using this rule of thumb with Fe-59

Consider using the same expression with **Fe-59**. Looking in data tables we will find the following gamma energies with their emission probability:

1.292 MeV (43.2%)

1.099 MeV (56.5%)

0.192 MeV (3.1%)

0.143 MeV (1.0%)

We could probably leave out the bottom lower energy gamma as its emission probability is also low. However we will use them all so you can see how this works. Considering E in the above equation, we now have the following:

E=(1.292 * 0.432)+(1.099*0.565)+(0.192*0.031)+(0.143*0.01) =**1.19**

Using exactly the same expression as above, but replacing (E) 0.662 (Cs-137) with 1.19 (Fe-59) we find that **D is 2204 micro Sv/h**.

Remember that the only difference is emission energy probability, the activity (M) is still 1 GBq (1000 MBq) and distance (r) is still 30 cm (0.3 m).

Now that we know how the above expression works, and it appears to provide reasonable values for Cs-137 in line with the literature, intuitively our value for Fe-59 (2204 micro Sv/h) should be about right.

- 1710 micro Sv/h per GBq at 30 cm (search result 1, online calculator)
- 1985 micro Sv/h GBq at 30 cm (search result 2)

Our value is a little higher than data obtained from a quick search online, but its still the right order of magnitude.

As with all our rules of thumb resource, use carefully and contact a Radiation Protection Adviser (RPA) if unsure.

#### Additional thoughts on this rule of thumb

If you have made it down to here you may well just be curious, or perhaps you are not so happy with the phrases such as '*pretty close*' or '*right order of magnitude*'?

Will will explore some of the finer technical details in a future blog post (will post the link here when completed). However, here are some things to think about.

**Its exposure in air**. The origin of the above expression is based on exposure rate (X) in air and has the units of R/h (roentgen/hour). Whilst many will consider 100 R = 100 RAD = 1 Gy = 1 Sv etc, this is a simplification and a loose use of radiation dosimetry units. In actual fact the R (now replaced with C/kg) is based on ionisation in air such that 1 R = 0.877 RAD (old non SI unit of absorbed dose). Since 100 RAD = 1 Gy, it follows that 100 R = 0.87 Gy (for x-rays and gamma rays in air under these specific conditions). Therefore, if the above rule of thumb actually outputs as 'exposure in air', then to reflect Gy (and Sv) correctly we would need to adjust the answer in 'micro Sv/h' by multiplying by 0.877. Trying this with the **Cs-137** dose rate we calculated above [1226 '*micro Sv/h*' * 0.877] = **1074 micro Sv/h**. This is now much closer to some of the reported data we listed. If we try with the **Fe-59** result we obtained above, [2204 'micro Sv/h' * 0.877] = **1933 micro Sv/h**, we are again much nearer the other reported data.

**Use of energy probability**. This is a lesson in not making assumptions. You will note above we explained how to deal with the energy (E) and emission probabilities for Fe-59. Well for Cs-137 we just made an assumption that its single 0.662 MeV gamma ray (actually from Ba-137m), was emitted with 100% probability. This is wrong, its actually 85.1% (Ref: NNDC). If we apply this emission probability to the now adjusted 1075 micro Sv/h for the Cs-137 (i.e. 0.662 MeV * 0.851) we find the dose rate reported is now 914 micro Sv/h using the activity and distance as before. We have no way of knowing, but it might be that others have also incorrectly set the emission probability for Cs-137.

**Use of a generic single average (μ _{en}/ρ)air** (mass energy absorption coefficient). By 'use' we mean built into the above expression (tied up in the '6'). We have deconstructed the rule of thumb and now know that the value of (μ

_{en}/ρ)air used is 0.03 cm

^{2}/g (air). We know that a more appropriate value is 0.0293 cm

^{2}/g for a photon energy of 0.662 MeV. If this value is used then our result for Cs-137 is

**845 micro Sv/h**and is then practically

__identical__to '

*search result 2, online calculator*' reported at the top of this page (848 micro Sv/h). We happen to think that this final value for Cs-137 is probably what you would actually measure under controlled conditions (and real measurement are always best).

The effect of using average 0.03 cm^{2}/g (air) is much more significant when using the rule of thumb with radioactive materials with lower emission energies. We will cover most of this in a future blog article, but in summary we tried the above rule of thumb with I-125. If you look at the energy and emission probability for I-125 you will find the follow:

0.035 MeV (6.5%)

0.027 MeV (112.5%)

0.031 MeV (25.4%)

Using the above rule of thumb formula, treating 'E' as before for multiple photon energies (see method used above for Fe-59), with an activity of 1000 MB and a distance of 30 cm, the dose rate calculated directly as before for **I-125** is **25 micro Sv/h**. A quick look online will indicate values much higher (e.g. 480-546 micro Sv/h). Something clearly does not look right here!! All becomes clear when you look at the cm^{2}/g (air) values for the I-125 energies. Compare the standard value of 0.03 cm^{2}/g (air) with what you actually should use in the calculation (in red below).

0.035 MeV (6.5%) (**0.11**)

0.027 MeV (112.5%) (**0.26**)

00.031 MeV (25.4%) (**0.153**)

This makes a significant difference to the calculation result and demonstrates that the rule of thumb would significantly underestimate dose rate for I-125 and other similar low energy gamma emitters. In an up and coming blog article we will show how the above values of u_{eu}/p in cm^{2}/g can be incorporated into the above rule of thumb, but by the time you have seen this you will probably want to use a reliable data book on online radiation safety calculator.

## The 10 half-life rule of thumb for radioactive materials

The 10-half-life reduction rule is an approximation but useful for evaluating contingency plans. It applies to all radioactive materials but is most useful for beta / gamma emitters with reasonably short half-life. The rule of thumb is as follows:

**10 Half-Life will lead to a thousand-fold reduction in activity (1/1000)**

For gamma emitters particularly, 10 Half-life will lead to a thousand-fold reduction in dose rate (all other variables being constant such as distance and shielding).

Mathematically, 1 / 2^{10} is 1/1024, but this is an approximation, so 1/1000 is good enough.

Now consider the following (after 10 half life).

- TBq becomes GBq
- GBq becomes MBq
- Sv/h becomes mSv/h
- mSv/h becomes micro Sv/h

**Practical example (F-18)**

A small vial of F-18 (positron emitter) is spilt on the floor of a laboratory. Dose rates taken 10 cm above the spill indicate **1000 micro Sv/h**. Should you clean the spill up now, or leave it to decay first? For the purpose of this rule we are only going to consider decay / dose rate, in real world situations there would be other things to think about (e.g. c*an the lab wait for the decay if it is preparing F-18 doses for patients required in a few hours time*).

The half life of F-18 is near enough 110 minutes. So 10 half life would take 1100 minutes or about 18 hours and 20 minutes. After this time, all other things being equal, the dose rate at 10 cm above the spill would have reduced to **1 micro Sv/h** (something much more manageable when considering occupational exposure). Even if 18 hours is not reasonably practicable, good dose saving can be achieved for every half life you are able to leave the spill before cleaning it up.