Harm from gamma radiation compared to beta radiation why is a small dose of gamma radiation less harmful than a small dose of beta radiation? even though gamma radiation is more penetrating.
This is a question I was wanting to know and had difficulty trying to research it, thanks.
 A: Without a clear definition of dose it’s hard to give a crisp answer. Let me try to give some general idea of the processes.
If you have a single gamma ray with an energy of 100 keV and project it towards the body, it will most likely penetrate several cm, Compton scatter a number of times, depositing a fraction of energy at each interaction. Finally it either escapes or its energy is fully absorbed. The lower-energy electrons that absorbed some of its energy will bounce around the tissue locally, causing ionization and potentially some damage to the DNA/RNA of cells. If these cells do not repair the damage, they may malfunction. If they furthermore are actively dividing, errors in the genetic code may show up in their “offspring”.
The key concept here is that the tissue as a whole may well survive because the damage is spread out - the cells’ ability to detect and correct local damage is quite good. This is the principle behind various kinds of radiation therapy: you irradiate a tumor from multiple directions; the treatment volume is exposed to the sum of all the radiation while the surrounding tissue gets only a fraction of the exposure (since the treatment beam only passed through the region for part of the time). Furthermore, by fractionating the treatment (maybe 1/30th of the total radiation needed in a single treatment session, and some time between sessions for the surrounding tissue to “repair”) the effect can be more localized.
These things suggest two things: gamma rays deposit their energy over larger areas (lower dose per unit volume) and below a certain threshold the body is capable of repairing itself (note - for radiation protection purposes the latter point is often ignored: in that field, 0.001 mSv / hour for 1000 hours is considered to be as harmful as 1 mSv/hr for one hour. Radiation treatment protocols suggest that is not quite true).
Contrast this to a beta particle (an electron). The stopping distance in tissue is extremely short, so it will do very local damage. All the ionization will be confined to just a few cells - the ability to correct the errors introduced is limited. By the above argument that would be problematic.
Of course a single particle is not likely to hurt the body. But if you aimed a narrow beam of N particles (gamma or beta) all with energy E at one part of the body (say, a spot on the hand), then the local ionization damage of the beta (deposited energy per unit volume) would be greater.
This is the principle behind certain cancer treatment protocols where microspheres or targeted molecules labeled with (for example) Lu-177 or Y-90 are deliberately implanted into a tumor: the beta radiation from the particles kills cells in the immediate vicinity without affecting tissue further afield (although the Bremsstrahlung of the decelerating electrons creates some secondary Xrays which do throw the energy to a larger region; they also allow visualization of the treatment with, for example, a gamma camera so the physician can ensure that the target volume is actually reached as intended).
This is a complex answer - bottom line is that a narrow beam of beta particles of a certain energy will deposit this energy in a smaller region, and because of the nonlinear effect of ionizing radiation on the body, this produces more significant local damage.
But one could write entire books on the subject to cover all the cases, exceptions, provisos. I hope the above is a useful start.
A: Beta radiation has a smaller penetration depth than gamma radiation. In the thinner parts of your body (like your hands), gamma radiation will go straight through, continuing out the other side. Most of the energy of the gamma rays will not be deposited. Beta radiation on the other hand will be stopped in your body. When the radiation is stopped, all of its energy is deposited inside you. The amount of energy deposited is what makes radiation dangerous. The energy will ionize electrons from the orbitals of atoms, breaking chemical bonds that should be there and forming chemical bonds that shouldn't be there.

A: 
why is a small dose of gamma radiation less harmful than a small dose of beta radiation

This is not true in general. If the doses are the same in units of rem or sieverts, then the definitions of the units have been carefully set up so that they're equally harmful in general.
However, the level of harm will depend on other details, which you didn't specify. For example, external exposure to low-energy betas might be harmless because the betas would be stopped by your clothing.
A: Because it is more penetrating, gamma radiation effects will be more dispersed.  While (as an example) 1mm of soft tissue might absorb (and receive the energy from) 100% of a particular alpha source, it might absorb only 10% of a gamma source. 
A: The key difference is in terms of ionisation potential. Beta radiation will ionise atoms that it passes, though not as strongly as alpha radiation. Gamma rays do not directly ionise particles, although they may cause particles they interact with to emit ionising radiation.
