# Calculating the integrated Beta dose in dense materials (radiolysis)

• solpete
In summary, radiolysis is the process of chemical decomposition caused by exposure to radiation, resulting in the breaking of chemical bonds and the creation of new molecules. In dense materials, this can lead to the production of highly reactive free radicals, causing significant damage and altering the material's properties. The integrated Beta dose is the cumulative amount of energy deposited by beta particles over a certain period of time, calculated by multiplying the average beta particle energy by the total number of particles and exposure time. It is important to calculate this dose in dense materials to understand the extent of radiation damage and determine appropriate measures for mitigation.
solpete
TL;DR Summary
I need to calculate the Beta dose deposited in plastic. Source is Co-60 or Cs-137. The question is relevant for radiolysis/degradation of plastic materials in a repository.
I have plastic which contains large amounts of Co-60 and Cs-137. I have already calculated the integrated (50k years) deposited dose from the gamma radiation using Monte-Carlo methods (SCALE).

I am now interested in the contribution to deposited dose from the Beta emissions.
-I am assuming that all Beta is stopped in the plastic itself.
-For Co-60, the average Beta energy is about E=0,31*(1/3) Mev.
-The conversion factor from MeV to Joules is C=1.6e-13 J/MeV.

Would the instant contribution to deposited dose in Gy (J/kg) per second from Co-60 Beta be:
E*C*I/m,

where I is the intensity in Bq and m is the mass?

Side note: Bremsstrahlung photons will also contribute to dose, but I have a feeling that this contribution is minor.

Peter, Phd

Last edited:
One would calculate the energy emitted from the 60Co and 137Cs. In one's problem, one wishes to calculate the dose in the plastic, so one must determine the mass of the radionuclides and then multiply by the ratio of mass of radionuclide(s) to the mass of the plastic.

anorlunda
Hello Peter, Phd,

Thank you for sharing your calculations and assumptions regarding the contribution of Beta emissions to the deposited dose from Co-60 and Cs-137 in plastic.

Based on your formula, the instant contribution to deposited dose in Gy (J/kg) per second from Co-60 Beta would be E*C*I/m. This formula takes into account the energy of the Beta emissions (E), the conversion factor from MeV to Joules (C), the intensity in Becquerels (I), and the mass (m) of the plastic.

I agree with your side note that Bremsstrahlung photons may also contribute to the dose, but it is likely a minor contribution compared to the Beta emissions.

Thank you for your contribution to the discussion on this topic.

## 1. What is radiolysis and why is it important in calculating integrated Beta dose?

Radiolysis is the process by which ionizing radiation breaks down molecules in a material, creating free radicals and other reactive species. These species can cause chemical reactions and potentially damage the material. In calculating integrated Beta dose, it is important to consider radiolysis as it can affect the accuracy of the dose measurement and the long-term stability of the material.

## 2. How do you calculate the integrated Beta dose in dense materials?

The integrated Beta dose in dense materials can be calculated by first determining the energy of the Beta particles, the density of the material, and the thickness of the material. Then, using the Bethe-Bloch equation, the stopping power of the material can be calculated. Finally, the integrated Beta dose can be calculated by integrating the stopping power over the thickness of the material.

## 3. What factors can affect the accuracy of integrated Beta dose calculations?

There are several factors that can affect the accuracy of integrated Beta dose calculations, including the energy and type of Beta particles, the density and composition of the material, and the thickness of the material. Additionally, the presence of impurities or defects in the material can also affect the accuracy of the calculation.

## 4. How does the integrated Beta dose in dense materials differ from other types of radiation dose calculations?

The integrated Beta dose in dense materials differs from other types of radiation dose calculations in that it takes into account the specific characteristics of Beta particles, such as their low penetration depth and high energy deposition. It also considers the unique properties of the dense material, such as its density and stopping power, which can affect the dose calculation.

## 5. What are some potential applications of calculating integrated Beta dose in dense materials?

The calculation of integrated Beta dose in dense materials has various potential applications, including in the field of radiation therapy to accurately measure the dose delivered to a tumor, in the nuclear industry to assess the radiation exposure of workers, and in the development of new materials for radiation shielding. It can also be used in research studies to better understand the effects of Beta radiation on different materials.

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