Level: Introductory, Intermediate

The Radiological Converter is a further development of Nucleonica’s Mass Activity Converter++ with the following additional features:

• The list of conversion quantities now includes a) Air Kerma Rates b) Exposure Rates and c) Ambient Dose Equivalent Rates H*(10) for approximately 1500 gamma and x-ray emitting radionuclides (depending on the database used).
• The threshold energy used in the calculations for dose quantities can be set by the user to investigate the effect of low energy photons on the dose calculations.
• Account is taken of short-lived daughter nuclides when a parent nuclide is selected.
• The underlying dataset used in the calculations can be selected from a list of international nuclear datafiles (JEFF3.1, ENDF/B-VII.1, 8th TORI)

In the example below, the nuclide Cs 137 is selected. The default source strength is 1 MBq. In the main Converter tab, below the Quantity/Unit input boxes, there is the information...

This informs the user that for the selected nuclide (in this case Cs 137) short-lived daughters have been included in the calculations (further details can be obtained by following the link). If short-lived daughters have been included, this is indicated by asterisk following the nuclide name in the grid (e.g. Physical Quantity Cs-137*) and before each of the entries in the grid (e.g. *Ambient dose equivalent rate at 1 m).

The option of including short-lived daughters can be de-activated in the Options tab.

Radiological Converter++ showing the data for Cs-137

Further details of the included daughter(s) can be seen in the Details tab as shown below.

Radiological Converter++ showing details of daughter(s) of Cs-137

## Inclusion of short-lived decay products in the evaluation of physical quantities

For the calculation of the dose rate constants, some nuclides are considered to be in equilibrium with daughter products. This is the case when a single radioactive decay chain in which radionuclides are present in their naturally occurring proportions, and in which no daughter nuclide has a half-life either longer than 10 days or longer than that of the parent nuclide, shall be considered as a single radionuclide. Such nuclides are denoted with an asterisk in the Nuclide Summary tab e.g. Cs-137*.

In the case of radioactive decay chains in which any daughter nuclide has a half-life either longer than 10 days or greater than that of the parent nuclide, the parent and such daughter nuclides shall be considered as mixtures of different nuclides.

## Nuclide Mixtures

The mass activity calculator can also be used for nuclide mixtures. In the diagram shown, the nuclide mixture “natural uranium” has been selected. This mixture has been previously created in the Nuclide Mixtures module for 1 mole (of atoms) of natural uranium containing:

U238: 0.992742 mole,

U235: 7.204x10–3 mole,

U234: 5.4x10–5 mole.

As can be seen, even 1 mole of atoms of natural uranium, with a mass of 238 gram and activity of approx. 6 MBq (*with daughters), has a negligible gamma dose rate and heat emission rate (isotopic power).

Radiological Converter++ showing the mixture Natural Uranium. Asterisk * denote short-lived daughters are included in the calculations

## Using the Module

### Nuclide Selector

In the Mass Activity Converter, the nuclide Co-60 is selected by default. A different nuclide can be selected from the element and mass drop-down menus. The Nuclide Chart Button: shows the location of the selected nuclide on the nuclide chart. To the right of this, the nuclide mixture link can be used to select a nuclide mixture.

The source strangth can be specified by using the drop-down menus (see the following section). The default source strength is 1 MBq.

In the Unit/Quantity drop-down menus, the source strength is shown in Becquerel (Bq), Curie (Ci), Number of Atoms, etc. This can then be convertd to other units.

Nuclide selector

### Quantity/Unit Selector

The input unit can be changed in the Unit drop down menu. The default unit is Bq. Had the value Curie been selected, on pressing the Convert button, the corresponding values in grams, Bq, number of atoms etc. are shown in the Convert to/Quantity table.

Convert to / Quantity Table

Once the unit and quantity have been selected in the Unit/Quantity Selector, the source strength in other units is given in the Convert to / Quantity table, by pressing the Convert button. The results are shown for 1 MBq Co-60.

### Options Tab

For the purpose of calculating the gamma dose rate, the distance from the source is required. The default distance used in the calculation is 100 cm. This value can be changed in the Options tab. The other default quantities used in this calculation are:

Medium: is vacuum

Radiations: both gammas and x-ray are taken into accounted

Threshold Energy: is 20 keV

(To obtain the gamma dose rate for different media, radiations and threshold energies, the Dosimetry and Shielding module should be used).

The various conversion factors user are:

Activity

1 Ci = 3.7 x1010 Bq

1 Bq = 60 disintegrations per minute = 60 dpm

Exposure

1 R = 2.58 x10-4 C/kg = 0.00877 Gy (in air)

Absorbed Dose

1 Gy (Gray) = 1 J/kg

Equivalent Dose

1 Sv (Sievert) = Absorber dose x Quality factor = 1 Gy x Quality factor

1 Sv = 100 rem

Effective Dose

1 Sv (Sievert) = Equivalent dose x Weighting factor

Once the various options have been selected, these settings can be stored for later use by clicking on Save to my defaults. The Nucleonca default values (shown in the figure) can be restored by clicking on Reset Nucleonica defaults. User defined options can be restored by click on Reset my defaults. If any of the values in the Options are changed for a new Search, the original saved default values can be recovered by clicking on the button Reset my defaults.

Options tab. showing the Nucleonica default values

### Mixture details Tab

When a nuclide mixture has been selected in the Radiological Converter, the information on the mixture can be see in the mixture details tab (shown). In the example shown, the selected nuclide mixture is "Transuranics in 1 ton Spent Fuel". This nuclide mixture has been created previously using the reactor simulation module webKORIGEN and contains neptunium, plutonium, americium and curium isotopes. The mixture details show the activity, masses, etc. of the nuclide components. Also shown is the total activity, mass, number of moles etc.

Mixture details tab. Asterisk * denotes short-lived daughters are included in the calculations

### Basic Quantities and Relationships

In this section, the basic relationships between number of atoms, mass, and activity, are developed. From these basic quantities, additional quantities such as the gamma dose rate, the effective doses for inhalation and ingesiton and the isotopic powers can be obtained.

For an amount of material with mass in grams given by $Mass(g)$,the number of atoms $N$ is given by

${N \over N_A} = {Mass(g)\over M}$ or $N = Mass(g) \cdot N_A/M$

where $N_A$ is Avogadro's number or Avogadro's constant ($N_A=6.02214179 \cdot 10^{23}$), and $M$ is the atomic mass of the nuclide. This basic relationship follows from the fact that 1 mole of any material contains Avogadro's number of atom.

The conversion of number of atoms to the number of moles is given by

number of moles $= {N \over N_A}$

The conversion from number of atoms to activity, and vice versa, is obtained using

$Activity(Bq) = k \cdot N = ln2 \cdot N/\tau$

$Activity(Ci) = Activity(Bq)/3.7 \cdot 10^{10}$

where $k$, and $\tau$ are the decay constant and half-life respectively of the nuclide. Combining the above relations, it follows that the relation between activity and mass is given by

$Activity(Bq) = (ln2/\tau) \cdot Mass(g) \cdot N_A/M$

### Derived Quantities

From the activity $A$, additional important quantities such as the gamma dose rate, the committed effective doses and the isotopic powers can be derived. The relations used in the Mass Activity Converter are given below. For more details on the meaning and derivation of these quantities, the reader should follow the links.

The committed effective doses are given by

Committed effective dose for inhalation, $E_{inh}(50) = e_{inh}(50) \cdot Activity(Bq)$

Committed effective dose for ingestion, $E_{ing}(50) = e_{ing}(50) \cdot Activity(Bq)$

Finally, the isotopic power (follow the link for a detailed explanation) is given by

Isotopic Power (α) $= A \cdot [E_{\alpha}]$

Isotopic Power (α + β) $= A \cdot [E_{\alpha} + E_{\beta}]$

Isotopic Power (α + β + γ) $= A \cdot [E_{\alpha}+E_{\beta}+E_{\gamma}]$

### Simple Decay and the Decay Constant

For simple radioactive decay processes in which a parent nuclide decays and there is no source term for the production of the parent, the equation for radioactive decay is given by:

$dN/dt = -k N$

where $N$ is the number of atoms at time $t$ and $k$ is the decay constant. The Activity is the number of disintegrations per unit time i.e. $Activity = -dN/dt = kN$. The decay constant is related to the half-life $\tau$ through the relation

$k = ln2/\tau$$0.693/\tau$

It follows that the number of atoms as a fuction of time is given by

$N(t) = N(0) \cdot e^{-kt}$ or alternatively $N = N(0) \cdot \left ( \frac{1}{2} \right )^{t/\tau}$

and the activity as a function of time is given by

$Activity(t) = Activity(0) \cdot e^{-kt}$ or altrnatively $Activity(t)=Activity(0)\cdot \left ( \frac{1}{2} \right ) ^{t/\tau}$

The expressions involving the term $\left ( \frac{1}{2} \right )^{t/\tau}$ are useful for calculating directly with the decay time $t$ and the half-life $\tau$.

## Exercises

Exercises using the Mass-Activity Calculator

1. Calculate the specific activities of C-14 and S-35?

(Ans. 1.7E11 Bq/g (4.5 Ci/g), 1.6E15 Bq/g (4.3E4 Ci/g)).

2. The activity of Sr-90 is 18,000 transformations per minute. What is the mass of Sr- 90?

(Ans. mass = 5.88E-11g).

3. 6 g of carbon from a piece of wood found in an ancient temple is analyzed and found to have an activity of 10 transformations per minute per gram (from C-14). How many atoms of C-14 are present in the sample and what is their mass?

(Ans. 2.6E11 atoms, mass = 6.0E-12 g)

4. The concentration of potassium (K) in humans is about 1.7 g/kg. How much potassium does an average person (weight 80 kg) contain? (136 g). What is the abundance of K-40 in natural potassium?. What is the mass and activity of K-40 in this person?

(Ans. 0.0117%,1.59E-2 g, 4.2 kBq)

5. What is the dose rate from a 100 MBq source of Co-60 at 2m distance?

(Ans.8.4 μSv/h)

6. What is the isotopic power of Sr-90? (Ans. 0.142 W)

What is the isotopic power of Sr-90/Y-90 in secular equlibrium? (Ans. 0.91 W)

For the solution to some of these exercises see Mass Activity Calculator solutions