A 75 kg laboratory technician working with the radioactive isotope 137Cs receives an accidental 100 mrem exposure. 137Cs emits 0.66 MeV γ-ray photons.
a) How many γ- ray photons are absorbed in the technician’s body?
b) How many rad of alpha radiation with an RBE of 10 will cause the same biological damage as the gamma ray above?
For a), I got 7.1 x 10^11 photons, am I correct?
I don't know how to solve for b)!!
Thanks
To calculate the number of γ-ray photons absorbed in the technician's body, we need to use the concept of absorbed dose and the given exposure.
a) Number of γ-ray photons absorbed in the technician's body:
1. First, we convert the exposure from millirem (mrem) to rem by dividing by 1000. Therefore, the exposure is 0.1 rem.
2. The absorbed dose is defined as the amount of energy deposited per unit mass of the material and is usually measured in rad (radiation absorbed dose).
3. To calculate the number of γ-ray photons absorbed, we need to convert the absorbed dose to energy. Given that the technician's mass is 75 kg, we can multiply the absorbed dose by the mass to get the total energy absorbed.
Energy absorbed (in Joules) = Absorbed dose (in rad) * Mass (in kg)
4. Since 1 rad is equivalent to absorbing 0.01 joules of energy per kilogram, we multiply the absorbed dose by 0.01 to get the energy absorbed.
Energy absorbed (in Joules) = Absorbed dose (in rad) * 0.01
5. Now we need to calculate the energy absorbed per γ-ray photon. The energy of each γ-ray photon emitted by 137Cs is given as 0.66 MeV, which is equivalent to 1.06 x 10^(-13) Joules.
6. Finally, divide the total energy absorbed by the energy absorbed per γ-ray photon to get the number of γ-ray photons absorbed.
Number of γ-ray photons absorbed = Energy absorbed / Energy absorbed per γ-ray photon
Let's calculate:
Absorbed dose = 0.1 rem
Mass of technician = 75 kg
Energy absorbed per γ-ray photon = 1.06 x 10^(-13) Joules
Energy absorbed = Absorbed dose * 0.01
Energy absorbed = 0.1 rem * 0.01
Energy absorbed = 0.001 J (Joules)
Number of γ-ray photons absorbed = Energy absorbed / Energy absorbed per γ-ray photon
Number of γ-ray photons absorbed = 0.001 J / 1.06 x 10^(-13) J
Number of γ-ray photons absorbed ≈ 9.43 x 10^9 photons
So, the number of γ-ray photons absorbed in the technician's body is approximately 9.43 x 10^9 photons.
Now, let's solve for b) to find out how many rad of alpha radiation with an RBE (Relative Biological Effectiveness) of 10 will cause the same biological damage as the given γ-ray exposure.
To compare the biological damage caused by different types of radiation, we use the concept of equivalent dose. The equivalent dose is calculated by multiplying the absorbed dose by the radiation weighting factor (RBE).
Equivalent dose (in rem) = Absorbed dose (in rad) * RBE
To find out how many rad of alpha radiation will cause the same biological damage:
1. Set up the equation using the equivalent doses for the γ-ray exposure and the alpha radiation.
Equivalent dose by γ-ray exposure = Equivalent dose by alpha radiation
Absorbed dose of γ-ray exposure * RBE of γ-ray exposure = Absorbed dose of alpha radiation * RBE of alpha radiation
2. Rearrange the equation to solve for the absorbed dose of alpha radiation.
Absorbed dose of alpha radiation = (Absorbed dose of γ-ray exposure * RBE of γ-ray exposure) / RBE of alpha radiation
RBE of γ-ray exposure = 1 (γ-rays are used as a reference for comparison)
RBE of alpha radiation = 10 (given in the question)
Let's calculate:
Absorbed dose of γ-ray exposure = 0.1 rem (from the previous question)
Absorbed dose of alpha radiation = (Absorbed dose of γ-ray exposure * RBE of γ-ray exposure) / RBE of alpha radiation
Absorbed dose of alpha radiation = (0.1 rem * 1) / 10
Absorbed dose of alpha radiation = 0.01 rem
Therefore, it would take an absorbed dose of 0.01 rem of alpha radiation with an RBE of 10 to cause the same biological damage as the given γ-ray exposure.
I hope this helps! Let me know if you have any more questions.