Question

Calculate range of alpha particles in air emitted by po-210

Answer 1

*Alpha and Beta Ranges*
By: Radiological71
31 March 2009

Alpha and Beta radiation are common types of radiation. The alphas and the betas have distinct properties, one of the most important is that they are little particles which are created with a starting velocity, and they slow down. Since they are continuously slowing down, eventually they will stop, and will have a finite range.

Alphas Particles

Alpha particles are the emitted by heavy isotopes and consist of two protons and two neutrons. Often an alpha particle is referred to as a Helium nucleus. The typical energy of an alpha particle is around 4 to 8 MeV. A MeV (pronounced Em ee Vee) is an abbreviation for a million electron volt of energy, which is not a terribly intuitive unit for most people. The MeV is a unit of energy, but an every day analogy might be to think of the weight of a car or a truck 1 ton is on the light side, and so is 1 MeV of particle energy. 10 tons of truck is respectable, so is 20 tons. By comparison 20MeV is a far whack of energy for most particles. Particle energies can go a lot higher, but you won’t find them around outside a laboratory or in outer space. This might sound like a fairly weird comparison, but when I was little, we always talked of “doing a ton” meaning travelling100 mph. If that’s still too weird, think of the radiation and ignore the energy: “that’s a 6 or a 7 alpha particle”.

Betas Particles

Beta particles are high energy electrons produced form radioactive isotopes. Most beta energies are less than 1 MeV, but there are a few higher energy beta particle emitters.

Both alpha particles and beta particles have an electric charge. This means that an alpha particle and a beta particle are continually influenced by the electrons of the material that they are traveling through. Because they are charged an alpha particle and a beta particle will continuously loose energy and slow down in any material. Because of that, beta particles and alpha particles have a finite distinct range.

Range in Air

The range in air of alphas and betas is estimated by various formulas.

Figure 1 presents the range in air of alpha particles and Figure 2 presents the range in air of beta particles. Different sources have been used, although they agree pretty well with each other. Alpha particles are much more massive than electrons, and so when they move through the air they tend to ionize everything. Because of this the alphas might start out with a lot more energy than a typical beta, but they will slow down and stop a lot faster.  Since most typical alpha particles are less than 10MeV, a rule of thumb would be a hand span away will remove the danger of most alpha particles. Beta particles will travel longer distances, up to a few meters so 20 feet is going to be the maximum range of any betas that we will encounter in practice. We should keep in mind that after such a long distance the betas will have lost a lot of energy, so their penetration in tissue will have fallen off quite a bit.

 
Figure 1 
Range in air of Alpha particles of various energies. The distance is in units of centimeters, and the energies are in terms of MeV.

 
Figure 2 
Range in air of beta particles. The distance is in units of centimeters, and the energies are in terms of MeV. Note how much longer beta particles will travel.

Examples

The maximum energy of beta particles form the isotope Phosphorous 32 is 1.710 MeV. What is its range in air?

Ans: From figure 2, the range in air of a beta particle of that energy is about 650 centimeters (roughly 20 feet).

Americium 241 (used in smoke detectors) emits alpha particles of energy 5.5 MeV. What is their range?

Ans: From Figure 1, the range of an alpha particle of 5.5MeV energy is about 4 cm in air.

Range in water

Water is a lot denser than air, and is a pretty common material. Most plastics are about the same density as water, and most solids are equal or denser than water. Humans are pretty close to water in average density too. So the range in water can be considered as a maximum worst case for shielding.

 
Figure 3 
Range of alpha particles in water. This displays the miniscule range of alpha particles in water. Note that the range is in millimeters.

 
Figure 4 
Range of beta particles in water.

Examples

Polonium 210 is sprayed all over the place from a radiological weapon. The energy of the alpha particles from Polonium 210 is 5.3 MeV. What range will these alpha particles have in water or skin tissue? Light cotton clothing about 1 mm thick is being worn by a person. Will alpha particles penetrate the cotton clothing?