# How to calculate absorbed dosage

Lets say you have some unstable isotope which decays via beta decay. For example, lets say you want to calculate the amount of beta radiation that is emitted from the decay of $^{87}\textrm{Kr}\to ^{87}\textrm{Rb}\to^{87}\textrm{Sr}$ where both decays are via beta- decay. I know how to calculate the radioactivity in mCi for each isotope in this decay at any arbitrary time. I know the half-lives and $Q$-value for each decay, but I'm not sure how to calculate the absorbed dosage in rad or gray. Is this a straightforward calculation? If not, where could I start reading to understand how to do it?

• The place to start is thinking about the definition of 'absorbed dose' and asking questions like "How much of the energy gets from the source to the victim?" and "How much of that is going to pass right through?". You'll need some basic familiarity with the Passage of Radiation Through Matter (PDF link, see the contents page). Jun 25, 2016 at 16:46

In my opinion there is no simple formula to calculate the dose in a very straight forward manner. To calculate the dose you have to calculate the energy deposition in a mass. For this you need range vs energy deposition curves. In the case of heavy particles they show a so called Bragg peak i.e. the energy is deposited at the end of range, electrons deposit their energy throughout their range. Hence to calculate the dose you need 1. range 2. energy deposition through the range 3. area of irradiation 4. density of the medium. With these quantities you can estimate the dose.

Now you need to convert RAD to REM, (Roentgen equivalent Man). Different particles have different weighing factors which indicates the damaging capability of those particles to human tissues on the absorption of same dose.

Now we talk about shielding, In the case of $\gamma$ rays the shielding mainly reduce the intensity of $\gamma$ rays and not their energy. However the shielding for particles mainly reduces their energy, and their number is reduced if shielding is longer than the range of particles.

Hence if you have shielding of $\beta$ particles their energy will reduce as well as their range and which reduces the affected volume.

You need to make or download numerical codes in order to calculate the doses. I think there is no simple way to do it. Scattering and absorption cross sections are available with NIST database.

I believe that my answer is not the full solution of your problem but it will show initial direction to achieve your goal.

Regards,

Absorbed dose for a given tissue or body organ can not be easily calculated using simple equations, even though it is simply defined as "amount of mean energy imparted per unit mass" , because it depends on so many other factors.

Absorbed dose for a given material can be measured using devices called as Dosimeters such as (Calorimeters, ion-chambers, or Film dosimeters, ets), but still with lot of correction factors.

Absorbed dose to a given material or medium depends on many factors such as type of charge particle, properties of medium,type of radiation interaction etc.

But as a standard procedure, you can calculate amount of energy absorbed to a some quantity of water by using a simulated software, but those requires good knowledge about Medical or Radiation physics.