## Technical note: How to calculate the conversion factor for Geiger tube SBM20

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## Problem and objective

There are a lot of publications on the Internet on how to convert CPM (Counts per Minute) obtained from a Geiger tube to radiation levels. However, despite the wide coverage of this topic on various forums and a wide range of examples with code for various programming languages, we had to understand the topic deeper than we wanted to in order to be able to properly calculate the conversion factor for Geiger tube SBM20 from CPM to absorbed dose of radiation μSv/h and configure the conversion in our own products and make an example calculation for everyone

IoT-devices, LLC is producing its Geiger counter module GGreg20_V3 with a pulse output and two types of tube to choose from. Currently, customers can choose either SBM20 or J305 when ordering a device from our production.

We plan to create separate documents for each of the popular tubes, and we are starting with a technical note on SBM20.

Therefore, in this document, we will look at the procedure for calculating the CPM to microsieverts per hour conversion factors for SBM20. For other common tubes, at least J305 and LND712, it will be covered later.

While collecting materials for this article, we came to the conclusion that this is not an easy task at all, because information is spreading on the Internet, which needs to be verified, and sometimes we even had to investigate where certain coefficients came from.

Let’s start with the useful information that manufacturers provide in their datasheets for their tubes.

## Solution

Let’s make calculations for SBM20 based on the manufacturer’s data:

Count rate at 4 μR/s from a Cs-137 source of pulses per second: 240 – 280;

1. Let’s take the average of these two values:

This is the average count rate at 4 μR/s from a Cs-137 source of pulses per second.

(240 + 280)/2 = 260 CPS / μR/s

2. Convert to pulses per second at 1 μR/s: μР/с:

260 / 4 = 65 CPS / μR/s

3. Convert to pulses per second at 1 mR/s:

65 * 1000 = 65000 CPS / mR/s

4. Convert to pulses per second at 1 mR/h:

round( 65000 / 3600) = 18 CPS / mR/h

5. Convert to pulses per minute at 1 mR/h:

18 * 60 = 1080 CPM / mR/h

6. Convert to pulses per minute at 1 μSv/h:

1080 / 10 = 108 CPM / μSv/h

or

108 CPM = 1 μSv/h

or

1 CPM = 1/108μSv/h

7. Calculate the value of one pulse per minute:

1 / 108 = 0,00926

Thus, if we need to convert the pulses recorded by the SBM20 tube during a minute into μSv/hour:

This is the value of the equivalent radiation dose recorded by the sensor – the SBM20 tube.

Please note that we took the average value of CPS / μR/s = 260 and obtained the value of CPS / mR/h = 18 by simple mathematical transformations.

We can also perform the above calculations not only for the average, but also for the minimum and maximum values specified in the data sheet for the tube: 240 CPS and 280 CPS at 4 μR/s.

In this case, we will get two additional values that we can also work with if necessary.

For convenience, let’s write them in CPS at 1 mR/h:

min value: 17 CPS / mR/h
max value: 19 CPS / mR/h

Let us summarize the results of our work at this stage of the calculation:

Everything would have been fine, and we could have stopped calculations there. But the coefficient we calculated, 0,00926

0,00926

only allows us to obtain the exposure value recorded by the Geiger counter. We are primarily interested in the equivalent dose of radiation absorbed by the human body.

Therefore, let’s move on to the next part of the calculations.

Although we are not a research institute, to solve our simple task we will have to dive into complex matters for a while.

In order to estimate the equivalent dose of energy absorbed by the human body, science uses the so-called human body phantom model, which calculates certain conversion factors for converting one value to another.

If you are interested in reading the theory on this subject, we can advise you to read this publication:

And we proceed to derive the conversion factor of the tube CPM into the equivalent dose of absorbed radiation in microsieverts per hour, taking into account the phantom model of the human body.

Let’s start the calculation with the already found coefficient of 18 CPS per 1 mR/h. Why is this so? Next, you will see that most tube manufacturers (J305 and LND712 included) provide parameters in this format in the datasheet for their products.

For example,

• for the J305 is specified in the datasheet: sensitivity of γ (60Co) cps/ mR/h 44
• for LND712: GAMMA SENSITIVITY CO60 (CPS/mR/HR): 18

where CPS – Counts per Second; mR – milli roentgen; h = hr – hours.

In the case of the SBM20 tube, the manufacturer specifies data for the Cs-137 source.

And we have already made the necessary conversions in the previous step:

Sensitivity of SBM20 to gamma rays: 18 CPS / mR/h 1.

1. Convert CPS to CPM at 1 mR/h (we already have this value, but we are going to calculate it again for the reader’s convenience):

18 * 60 = 1080 CPM / mR/h

2. Convert CPM at 1 mR/h to CPM at 1 R/h:

1080 * 1000 = 1080000

3. Find the value of the exposure dose R/h per 1 CPM:

1 / 1080000 = 0,0000009259259259

4. Find the air kerma (Ka, kinetic energy released per unit mass / in matter):

The equation is as follows:

Ka [Gy] = 0.00877 [Gy/R] x exposure [R]

where 0.00877 is the coefficient of radiation dose absorption by the human body on the phantom model under the influence of photon energies of 100 keV – 3 MeV

0,00877 * 0,0000009259259259 = 0,00000000812037037 Ka[Gy]

5. Convert Ka[Gy] to Ka[uSv] (i.e., switch from Gray to µSv):

0,00000000812037037 * 1000000 = 0,00812037037 Ka[uSv]

6. Perform the check and find the inverse value:

0,00812037037 ^(-1) = 123,1470924

Thus, the formula for the equivalent absorbed dose of radiation by the human body for the Geiger-Muller tube SBM20 with gamma sensitivity for Cs-137 of 18 CPS / mR/h is as follows:

where

0.00812 μSv/h is the value of one count, CPM;

CPM – number of counts per minute.

We can also calculate the coefficients for the minimum and maximum CPS / mR/h values provided by the datasheet:

At the same time, the Internet uses a coefficient of 175.43 (0.0057), which, as can be seen, does not fit into the calculations above. However, this coefficient is similar in value to the data for SBM20 for Ra-226 taken from the Internet:

In order for the CPM to uSv/h conversion factor to be 0.00570, the initial value of CPS/mR/h in the tube datasheet should be 25.643. We determined this by the simple value adjustment (25.643 * 60 / 8.77 = 175.4367; 1 / 175.4367 = 0.00570).

Another popular coefficient for the SBM20 tube is also published on the Internet: 150.5131 (0.00664), allegedly calibrated to Co-60. We do not know where this information came from.

What else can we do to try to find the 0.0057 coefficient that is used everywhere for SBM20?

### Switching from coefficients for Cs-137 to Co-60

We can try to move from the values at Cs-137 (which is indicated in the tube documentation) to Co60, which is now the most commonly used standard for calibrating Geiger-Muller tubes in the world.

To do this, it is necessary to calculate the conversion factor for Cs-137 to Co-60 values.

Let’s take the average value for the two Co-60 energy lines:

Co-60: 1.1732 MeV; 1.3325 MeV; Average value: 1.25285 MeV

And the energy value of Cs-137:

0.6617 MeV

Let’s find the energy ratio of Co-60 to Cs-137:

1,25285 / 0,6617 = 1,893380686

Next, we calculate the corresponding value of CPS at 1 mR/h:

18 * 1,893380686 = 34,08085235

Assuming that this value is indicated in the data sheet for the tube, we will calculate the new coefficient of the absorbed equivalent dose of μSv/h per 1 CPM for Co-60:

34 CPS / mR/h

1. Convert CPS to CPM at 1 mR/h:

34 * 60 = 2040 CPM / mR/h

2. Convert CPM at 1 mR/h to CPM at 1 R/h:

2040 * 1000 = 2040000

3. Find the value of the exposure dose R/h per 1 CPM:

1 / 2040000 = 0,0000004901960784

4. Find the air kerma (Ka, kinetic energy released per unit mass / in matter):

The equation is as follows (as in the previous calculation):

Ka [Gy] = 0.00877 [Gy/R] x exposure [R]

So:

0,00877 * 0,0000004901960784 = 0,000000004299019608 Ka[Gy]

5. Convert Ka[Gy] to Ka[uSv] (i.e., switch from Gray to µSv):

0,000000004299019608 * 1000000 = 0,004299019608 Ka[uSv]

uSv/h = CPM x 0,00429 for Cs-137->Co-60

### Switching from coefficients for Cs-137 to Ra-226

We calculate the conversion factor from Cs-137 to Ra-226 in a similar way:

Because Ra-226 has several energy lines of gamma radiation:

186.2 кеВ;
240.3 кеВ;
295.2 кеВ;
352.0 кеВ;
609.3 кеВ;
657.0 кеВ;
768.4 кеВ;
934.8 кеВ.

we will select all of them that can be detected by the SBM20 tube. According to the documentation, the SBM20 is sensitive to gamma quanta from 0.05 MeV to 3 MeV.

Therefore, all of these lines fall within the detection range. In order to move from Cs-137, we need to either work with the average of these lines or select the line most characteristic of Ra-226.

If we need to rely on a specific line to identify a radionuclide, we need to take into account the intensity and energy of this line. Usually, the so-called “characteristic peak” is used to identify a radionuclide, which is the most intense and is located at the most characteristic energy for this radionuclide.

In the case of the gamma spectrum of Ra-226, which consists of several lines, the characteristic peak can be determined by the highest intensity and energy of the line. According to the table of line intensities of the Ra-226 gamma spectrum, the line with an energy of 609.3 keV is the most intense line, so this line can be used to identify Ra-226.

The average value of the energies of all lines of the gamma spectrum of Ra-226 can also be determined, but it is not useful for identifying the radionuclide. However, the average value is useful for determining the average gamma energy of a given radionuclide.

The table of line intensities and energies can be used to calculate the average gamma energy of Ra-226.

Let’s calculate the sum of the energies of all lines of the Ra-226 gamma spectrum:

0.186 MeV + 0.244 MeV + 0.295 MeV + 0.351 MeV + 0.609 MeV + 1.061 MeV + 1.158 MeV + 1.332 MeV = 5.196 MeV

Divide the sum of energies by the number of lines to get the average energy:

5,196 MeV / 8 = 0,6495 MeV

Thus, the average gamma energy of the Ra-226 radionuclide is approximately 0.65 MeV. Note that this value is only an average energy and may differ from the individual values of the gamma spectrum lines.

Now we have three alternative values that we can use to find the conversion ratio from Cs-137 to Ra-226 calibration. The third option is the weighted energy value provided on the hps.org website.

1. Characteristic peak: 609.3 keV [peak];

2. Average energy of gamma radiation: 0.6495 MeV [avg];

3. Weighted value of gamma radiation energy: 0.74 MeV [wght].

Let’s calculate the corresponding energy ratios:

Cs-137 energy value: 0.6617 MeV.

Find the energy ratio of Ra-226 and Cs-137:

peak: 0,6617 / 0,6093 = 1,086000328245528
avg: 0,6617 / 0,6495 = 1,018783679753657
wght: 0,74 / 0,6617 = 1,118331570197975

Next, we will calculate the corresponding value of CPS at 1 mR/h, i.e., we will move from the Cs-137 calibration, as indicated in the datasheet, to the calculated calibration value relative to Ra-226:

peak: 18 * 1,086000328245528 = 19,5480059084195
avg: 18 * 1,018783679753657 = 18,33810623556582
wght: 18 * 1,118331570197975 = 20,12996826356355

As we can see, the attempt to switch from Cs-137 to Ra-226 did not give us anything either, because we could not get the target CPS value of 25.643/mR/h, at which it is possible to obtain a coefficient of 0.00570.

The coefficient of 0.00429, which we obtained earlier for the case of Cs-137->Co-60, is also not similar to the common one for SBM20 175.43 (0.0057). Therefore, we can only guess where the Internet contributors got it from and use the one we obtained above by calculations based on the information in the datasheet for the tube.

Note . If you thought that we did not check the datasheets of the modern production SBM20 and only rely on outdated Soviet data, this is not the case. We have checked all possible sources available on the Internet. SBM20 tubes produced in 2021 and later have different calibration options in their documentation:
78 imp/μR without specifying a source (1/150.5131129, or 0.006643);
– 105 imp / µR at Ra-226 (1 / 198.4036488, or 0.005040);
67.5 imp/μR at Cs-137 (1 / 129.9885975, or 0.007692);
None of the documents we studied contains source data that could lead us to the coefficient of 0.0057 μSv/h at 1 imp/min.

As a reminder, our recommended formula for the equivalent radiation dose absorbed by the human body for the Soviet Geiger-Muller SBM20 tube with a gamma sensitivity of 18 cps/mR/h for Cs-137 is as follows:

where

0.00812 μSv/h is the value of one count, CPM;
CPM – number of counts per minute.

## Conclusions

In this article, we have provided a detailed step-by-step calculation of the conversion factor for the data transmitted by the Geiger counter with the SBM20 tube and figured out what factor we need to apply in order to not only get the level of exposure dose recorded by the sensor, but also the dose absorbed by the human body.

Unfortunately, we could not figure out where the magic coefficient of 0.0057 μSv/h per 1 CPM, which everyone uses, came from. Neither mathematical transformations, nor the transition from Cs-137 to Co-60, nor the transition from Cs-137 to Ra-226, nor the adjustment of the coefficient (in particular, 8.77, 0.94 to 0.98) of the absorption dose for the phantom model of the human body gave the desired results. It seems that this is a special case that someone, at some point, simply accepted their calculations and did not leave instructions for us.

Please write to us if you have your own version of where 0.0057 came from or a good calculation on this topic. We will be grateful and will make appropriate additions to this post.

At the same time, we were able to find a mathematically sound calculation of another magic coefficient

8.77,

which is used to obtain the value of the radiation dose absorbed by the human body. Now you also know where it comes from.

Currently, for soviet tubes, we recommend that instead of the coefficient of 0.0057, use the coefficient that we calculated for the equivalent dose of radiation absorbed by the human body:

where

0.00812 μSv/h is the value of one count (CPM) for the SBM20 tube calibrated against the Cs-137 source;
CPM – number of counts per minute.

If your SBM20 tube has a different sensitivity factor in the documentation, or if your tube is calibrated by the manufacturer against a different radioactive source, we recommend that you use the data for your tube.

In the next publications for J305 and LND712 tubes, there will be a little less text, because almost all coefficients published on the Internet correspond to our calculations.

And we have not yet covered the topic of internal background (false-positive) pulses for Geiger tubes. The work is not over yet!

Stay tuned!