How is radioactivity absorbed in the air?

Question

I am trying to make a computer game, which involve radioactive hazard. The game is still in its early stage, and I want to add mechanisms which are as realistic and as fun as possible.

So I'm trying to understand how radioactivity is "absorbed" in the air.

For example (please excuse any physic mistake), if you have some alpha radioactivity, it will be absorbed by a very thin material, like a sheet of paper. For Beta, it's more like an aluminium sheet, and for gamma you're dead already.

But how does the radioactivity weaken in the air ? Is it absorbed by random elements and the energy is lost in them ? I guess the explanation is similar to why Wifi just doesn't work at great distance, but then I'm not sure how it happens.

Feel free to give any text explanation, however I'm open (even if a bit afraid) of mathematical explanation. I'm pretty sure there is a theorem or something about this, this would be even better (although explanation won't hurt).

Answer 1

To a first approximation, radioactivity weakens in the same way in all types of matter, whether solids, liquids, or gases. The only difference is thickness is required to attenuate the intensity of the radiation, and this is largely a function of the density of the material. The particles making up the radiation (helium nuclei for alpha, electrons for beta, and photons for gamma) lose energy by colliding with atoms. Radiation particles collide with atoms more often in denser materials, so they lose more energy in less distance. The shielding for such radiation is often lead (Pb), not because there's anything special about the material, but because it's one of the densest cheap materials there is, so you don't need a large volume. If you want to use less dense aluminum, you need the same mass to provide the same shielding as lead, so a much thicker block of aluminum is required.

For your game, given a certain radioactive source you have two variables determining for how quickly radiation damages PC or NPC: distance and shielding.

Say you have a rock made of radioactive ore sitting on the ground. The further away the character is, the safer they are. Specifically, the amount of damage done falls off as the square of the distance (double the distance is one-fourth the damage rate). So, $$D \propto \frac{1}{r^2}$$ where $D$ is the rate of damage, $r$ is the distance from the source to the character, and $\propto$ means "proprotional to."

Second, shielding attenuates radiation in an exponential fashion. $$D \propto e^{-k\rho{}x}$$ where $e$ is ~2.718 (the natural logarithm base), k is a constant dependent on the radiation type, $\rho$ is the density of the shielding material, and $x$ is the distance the radiation travels through--that is, the thickness of the shielding. If you have more than one shield material, you can get the average density by weighting the density of each shielding type: $$\rho_{avg} = \frac{\sum_i \rho_ix_i}{\sum_i x_i}$$ where $\rho_i$ is the density of the $i^{th}$ material and $x_i$ is the thickness of the $i^{th}$ material. For example, if there is 2 meters of air and 2 cm of lead between the radiation source and a character, the average density of the shielding is $$\frac{\rho_{air}(2 m) + \rho_{lead}(0.02 m)}{2.02 m}.$$

In total, the rate a radioactive source damages a character is given by $$D = A\frac{e^{-k\rho x}}{r^2}$$ where $A$ is a constant indicating the inherent radioactivity of the rock, which is a function of how much radioactive material there is and how often its atoms decay.

There are a lot more details that could be discussed (the many ways radiation loses energy, how different materials modify the exponential falloff, etc.), but for making a game, I think this simple model should suffice.

Answer 2

The basic idea behind radioactivity is that a radioactive element will emit radiation or particles (sometimes for hundreds of thousands of years) until it turns into a stable element, so for example, potassium-40 will radioactively decay to  argon-40.

This radiation will sometimes ionize air, removing an electron from an oxygen or nitrogen molecule. So you get say, an oxygen molecule that is missing an electron, or is moving / vibrating/ rotating slightly faster, ( depending on the amount of energy it receives).

The oxygen molecule will then look regain an electron, or pass it's extra energy of vibration by means of photons, until the original radioactive energy is spread among so many molecules of air, it is undetectable.

Your piece of paper will also do the same job, absorbing low energy particles and having its electrons slightly shook by the incoming energy.

Following Jon's comment below, it should be noted how the penetrative power changes with the type of radiation involved.

From Wikipedia Radioactive Decay

Alpha particles generally have a kinetic energy of about 5 MeV, and a velocity in the vicinity of 5% the speed of light. They are a highly ionizing form of particle radiation, and (when resulting from radioactive alpha decay) have low penetration depth. They are able to be stopped by a few centimeters of air, or by the skin.

Beta decay (β-decay) is a type of radioactive decay in which a beta ray (an energetic electron or positron) and an associated antineutrino or neutrino are emitted from an atomic nucleus. Beta rays can penetrate several millimetres of aluminium.

Gamma rays (radiation) is extremely high-frequency electromagnetic radiation and therefore consists of high-energy photons. Shielding from gamma rays requires large amounts of mass. Gamma rays are better absorbed by materials with high atomic numbers and high density, although neither effect is important compared to the total mass per area in the path of the gamma ray. For this reason, a lead shield is only modestly better (20–30% better) as a gamma shield than an equal mass of another shielding material, such as aluminium, concrete, water or soil; lead's major advantage is not in lower weight, but rather its compactness due to its higher density.

From Half Life Wikipedia

The half-life of a substance is the time it takes for half of the substance to decay. The word "half-life" was first used when talking about radioactive elements where the number of atoms get smaller over time. It is now used in many other situations. A Geiger-Muller detector can be used to measure the half-life; it is the time when the activity is half of the original.

Note that half-life is defined as a probability. Half-life is the expected value when half the number of atoms have decayed. Carbon-14 has a half-life of 5730 years. Taking one atom of C-14, this will either have decayed after 5730 years, or it will not. But if this experiment is repeated again and again, it will be seen that the atom decays within the half life 50% of the time.