Radiation Dose Rate from 60Co γ-Ray Source

[Hazzattack]

Homework Statement

Some people are standing at a distance of 3 m from an unshielded 60Co γ-ray source of activity
10^9 Bq. What radiation dose rate are they receiving? (Each disintegration of 60Co produces a
β particle of 0.3 MeV maximum energy with a range 0.8 m in air, and two γ rays, one of 1.2 MeV and one of 1.3 MeV, in quick cascade).

Homework Equations

dDose/dt = AE/r^2

A = activity
E = energy of photons
r = distance from source

The Attempt at a Solution

I'm at a bit of a loose end with this question as I've not been given any guidance - perhaps someone could suggest a relevant website to explain?
Due to the Beta particle traveling only 0.8m does this mean it doesn't reach the people standing 3m away? or does it decay into other particles?
Do i at some point calculate the flux of the rays? as i put the r^2 term in as i assumed it to be like a point source and diverging away (thus a 1/r^2 relation)

Thanks for any help and guidance on this question!

 

[mfb]

Due to the Beta particle traveling only 0.8m does this mean it doesn't reach the people standing 3m away?

Right. An electron is an elementary particle, it cannot decay. It can produce Bremsstrahlung (photons), but that can be neglected I think - even if its total energy would be converted to Bremsstrahlung, 0.3 MeV << (1.2 MeV + 1.3 MeV).

as i put the r^2 term in as i assumed it to be like a point source and diverging away (thus a 1/r^2 relation)

That is fine for the radiation per area. You might need some additional conversion to get a radiation dose rate for those humans.

 

[Hazzattack]

Ok... so do i just multiply it by the approximate area of a human?

I would have Radiation/area * area(of human) = radiation dose/per time(comes from the activity)

 

[mfb]

If humans absorb every photon which hits them, right. As an upper estimate, this should be fine.

 

[daveb]

This is a poorly worded question and you should tak your instructor (or the editor of the book) to task. The formula is (usually) the exposure rate, not the dose rate since not all gammas that pass through the body will be absorbed completely. In addition, the inverse square law applies only to point particles or geometries that approximate point particles.