# How do I convert TVT (10th value thickness) values to attenuation for Gamma or X-ray sources of radiation?

Source: Ionactive Consulting Radiation Protection Resource

For this resource article it is assumed that you know the basics of the TVT (10th Value Thickness) for simple gamma and x-ray shielding requirements. This is very briefly summarised below, but you may wish to visit our glossary entry: 10th Value Thickness (TVT) and our rules of thumb and FAQ guidance: How do I convert TVT to HVT (or the other way around)?

In summary, the TVT (sometimes denoted 10th Value Layer or TVL) is the thickness of material that is required to reduce radiation dose rate (or dose) to 1/10 of the pre-shielded value. As seen in the above referenced links, you can add TVT thickness and multiply the attenuations as follows:

1TVT + 1TVT = 1/10 x 1/10 = 1/100

For Cs-137 using lead, the TVT for lead is 22mm. Therefore 2 TVT would be as follows:

Note on attenuation. For the purpose of this resource article we take a very simple and literal definition which is simply means by how much a radiation dose rate / dose is reduced (attenuated). We are not considering the physics of mass attenuation coefficients, absorption, scattering or the mechanisms of radiation attenuation through matter. This resource considers the practical use of TVT and how it attenuates dose rate (or dose).

Question: For Cs-137 (see above), how many TVT are in 78mm of lead, and what attenuation would this provide? If you look carefully it is somewhat more than 3TVT (66mm) but not as much as 4 TVT (88mm). This is a simple problem to solve and takes the usefulness of the TVT a little further.

#### How many TVT have we got?

This is just simple division as follows:

78mm (what we have) / 22mm (the TVT) = 3.5454

#### What attenuation does this provide?

The general expression to use is as follows:

10(-TVT) = attenuation. To be convinced, try it first with whole TVTs and see how it works. You type this directly into a calculator as shown below, or use the xy key.

10(-1) = 0.1 (1/10) 1TVT

10(-2) = 0.01 (1/100) 2TVT

10(-3) = 0.001 (1/1000) 3 TVT

Finally, try with our Cs-137 and lead example above. Recall we had 3.5454 TVT.

10(-3.5454) = 0.0002848 or 2.848 x 10-4 if you prefer (with some rounding)

You can see that the result, 0.0002848, is somewhere between 0.001 (3TVT) and 0.0001 (4 TVT) as expected.

#### How do we convert from attenuation back to TVT?

For this we will stick with Cs-137 and lead (which had a TVT of 22mm).

Question. We have Cs-137 source emitting 777 μSv/h at a certain distance. We only want this to be 20 μSv/h, and for the purposes of this example we want it as near 20 μSv/h as we can achieve.

First consider the amount of attenuation required. This is just a simple division as follows:

Attenuation required = μSv/h (what we want) / μSv/h (what we have)

So, attenuation required = 20 μSv/h / 777 μSv/h = 0.02574

The number of TVT can be calculated from the following simple expression:

TVT = -(Log [Attenuation])

As before, try this with some simple numbers first to be sure you believe the results. Use a calculator and be sure to use the minus (-) exactly where it is shown above.

For an attenuation of 1/10 (0.1) we have -(Log [0.1]) = 1 (TVT)

For an attenuation of 1/100 (0.01) we have -(Log [0.01]) = 2 (TVT)

For an attenuation of 1/1000 (0.001) we have -(Log[0.001)] = 3 (TVT) ... and so on.

Returning to our value of 0.02574 in our Cs-137 problem outlined above we have:

-(log[0.2574]) = 1.5894 TVT (with some rounding).

Noting that the TVT for lead (with Cs-137) is 22mm, it follows that:

Lead required = 1.5894 x 22mm = 35mm (rounded up).

Caution - this example shows how the maths works. We have not discussed distance, or placement of the lead shielding around the source, in other words the "design" of the shielding. This simple method will tend to overestimate the shielding required.

#### What are the expressions for converting TVT to attenuation or attention to TVT?

10(-TVT) = attenuation. [Convert TVT to attenuation].

TVT = -(Log [Attenuation]) [Convert attenuation to TVT].

#### How do I convert HVT (1/2 value thickness) to attenuation ?

This can be done in a similar way. Note the following (which is detailed in the links given at the top of this article):

1 HVT = 0.5 attenuation

1 HVT + 1HVT [2 HVT] = 0.5 x 0.5 = 0.25 (1/4) attenuation

1HVT + 1HVT + 1HVT [3 HVT] = 0.5 x 0.5 x 0.5 = 0.125 attenuation

Generally the following expressions can be used

0.5(HVT) = attenuation

Try this first with 3HVT. We have

0.5(3)= 0.125 (which is expected for 3HVT as shown above)

If you have followed the links at the start of this article you will have seen that 3.32 HVT = 1 TVT (i.e. conversions between the two). We can use the above expression to check that this makes sense as follows.

0.5(3.32) = 0.1001 (so 0.1 for practical purposes). We know that 1TVT will provide an attenuation of 0.1 so we have just proved the HVT to TVT conversion is as expected.

If you start from nothing, it is very difficult to get anywhere

– Gerhard Herzberg -