Which of these radiation sources gives a higher dose rate?

[LennoxLewis]

Both are point sources.

Source A emits 500 KeV gamma-rays, while source B emits betas, with maximum energy of 500 KeV. Assume that the sources have equal activity, the same range, and are close enough for absorption of betas in air not to be a factor. Which gives the higher external dose rate for a worker?

My guess is that it would be the betas because they get stopped by a cm of skin, if that, while some of the gammas might go through and do not deposit all of their energy? Would there be a large difference?Sidenote, this is NOT taking into account the fact that dose absorbed by the dead skin layer (600 um on the hands?) is not so relevant

 

[Vanadium 50]

Every gamma has an energy of 500 keV. What do we know about the energy of betas?

 

[Lok]

Beta radiation can be easily stopped by the clothes you are wearing while gamma might pass through you or just kick a few electrons and break some DNA to create a bit of cancer.

 

[LennoxLewis]

Every gamma has an energy of 500 keV. What do we know about the energy of betas?

That their maximum energy is 500 KeV. So, that's probably an average of 160 KeV.

 

[Vanadium 50]

So which would give a higher dose rate?

 

[LennoxLewis]

Well, the betas may have less energy, but they deposit 100% of it, whereas gamma's might pass through, say, your arm, and not lose all their energy to the photo/Compton effect. So i think betas give a higher dose rate.

 

[Bob S]

The first interaction of a 500 KeV gamma is probably an inelastic Compton scattering, followed by another, and eventually entirely absorbed by a (photoelectric) deep core electron photoejection. In every case, the energy loss to tissue is due to ionization by stopping electrons. So the penetration of the 500 KeV gamma is more, and the ionization process occurs over a larger volume.

 

[Vanadium 50]

whereas gamma's might pass through, say, your arm, and not lose all their energy to the photo/Compton effect.

Why do you suppose that? At 500 MeV, the photon-nucleon cross-section is at maximum, so the effective radiation length is of order 5 cm.

 

[LennoxLewis]

Why do you suppose that? At 500 MeV, the photon-nucleon cross-section is at maximum, so the effective radiation length is of order 5 cm.

Alright, so if both deposit all their energy, then they should yield an equal dose rate under those circumstances?

 

[jambaugh]

I really think you can't compare external doses as the type of exposure is different. At best one might compare lethal levels of internalized sources of beta and gamma resp. That defines an empirical comparison somewhat independently of the penetrating power of the radiation itself.

 

[LennoxLewis]

The thing is, i used an approximation formula which seems fairly valid under these circumstances, which gave a beta dose rate about 100 times higher than the gamma. The radiation syllabus confirmed this. I've gone over the number and they seem correct, i just can't figure out WHY!

 

[Bob S]

Why do you suppose that? At 500 MeV, the photon-nucleon cross-section is at maximum, so the effective radiation length is of order 5 cm.

My table shows that the total absorption cross section for 100 MeV photons in water is about 0.018 cm² per gram, corresponding to about 55 cm. My table shows the radiation length for water is 36 cm. I thought the maximum photonuclear croass section (giant resonance) was ~15 MeV (i.e., for (gamma,n) interaction etc). Anyway, we should be talking about 500 Kev photons, well below pair production threshold. At 500 KeV, the photon absorption cross section in water is about 0.1 cm² per gram, due nearly entirely to Compton scattering.

 

[Bob S]

The thing is, i used an approximation formula which seems fairly valid under these circumstances, which gave a beta dose rate about 100 times higher than the gamma. The radiation syllabus confirmed this. I've gone over the number and they seem correct, i just can't figure out WHY!

You are correct. The beta ray (electron) itself immediately ionizes tissue as it stops. Photons do not ionize, but instead have to interact with tissue via Compton scattering to produce ionizing electrons. The 500 KeV photon penetration length (1/e attenuation length) is roughly 10 cm in tissue.

 

[Vanadium 50]

My table shows that the total absorption cross section for 100 MeV photons in water is about 0.018 cm² per gram

And if you look at the gamma-photon cross-section you see it peaks at 500 MeV, and is several times larger there than it is at 100 MeV.

 

[Vanadium 50]

Alright, so if both deposit all their energy,

Are the energies the same?

 

[LennoxLewis]

You are correct. The beta ray (electron) itself immediately ionizes tissue as it stops. Photons do not ionize, but instead have to interact with tissue via Compton scattering to produce ionizing electrons. The 500 KeV photon penetration length (1/e attenuation length) is roughly 10 cm in tissue.

True, but my understanding was that while photons are indirectly ionizing, when one takes into account u(tr)/roh, i.e. the fraction of ionisations a photon causes per interaction, it should be equal?

Are the energies the same?

Well, the betas have to share their energy with neutrino's, so their energies are somewhere between 0 and 500 KeV, average probably about 160 KeV. The gammas are monoenergetic, at 500 KeV.

 

[Vanadium 50]

Well, the betas have to share their energy with neutrino's, so their energies are somewhere between 0 and 500 KeV, average probably about 160 KeV. The gammas are monoenergetic, at 500 KeV.

So be careful of any conclusions that relies on equal energies.

 

[Bob S]

True, but my understanding was that while photons are indirectly ionizing, when one takes into account u(tr)/roh, i.e. the fraction of ionisations a photon causes per interaction, it should be equal?
Well, the betas have to share their energy with neutrino's, so their energies are somewhere between 0 and 500 KeV, average probably about 160 KeV. The gammas are monoenergetic, at 500 KeV.

You are correct on both counts. In both cases, all of the energy loss is due to ionizing electrons. This is the basis for the Bethe-Bloch energy loss equation. On this basis, the 500 KeV gamma produces roughly 3 times the total ionization of a 160 KeV beta-ray (if it is an electron, not a positron). But the energy deposition density of the 500 KeV gamma is less, because of the penetration depth of the photon.

 

[LennoxLewis]

So be careful of any conclusions that relies on equal energies.

Well, my original point was that the betas have LESS energy, but induce a higher dose, and i was wondering exactly why.

You are correct on both counts. In both cases, all of the energy loss is due to ionizing electrons. This is the basis for the Bethe-Bloch energy loss equation. On this basis, the 500 KeV gamma produces roughly 3 times the total ionization of a 160 KeV beta-ray (if it is an electron, not a positron). But the energy deposition density of the 500 KeV gamma is less, because of the penetration depth of the photon.

I see. So it is due to a higher interaction density after all... i actually think this is rather interesting, considering photons and betas both have a radiation quality factor of 1!

 

[Bob S]

True, but my understanding was that while photons are indirectly ionizing, when one takes into account u(tr)/roh, i.e. the fraction of ionisations a photon causes per interaction, it should be equal?.

Dose is (was?) was defined as 1 rad = 1 erg per gram (of tissue), with a quality factor thrown in for neutrons. Because it is ergs per gram of tissue, the concentration of dose has to be figured in. So the 500 KeV peak beta rays probably have the higher dose rate.