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Ionization and Range

Ionization and Range

Two of the most important characteristics of \(\alpha \), \(\beta \), and \(\gamma \) rays were recognized very early. All three types of nuclear radiation produce ionization in materials, but they penetrate different distances in materials—that is, they have different ranges. Let us examine why they have these characteristics and what are some of the consequences.

Like x rays, nuclear radiation in the form of \(\alpha \) s, \(\beta \) s, and \(\gamma \) s has enough energy per event to ionize atoms and molecules in any material. The energy emitted in various nuclear decays ranges from a few \(\text{keV}\) to more than \(\text{10 MeV}\), while only a few \(\text{eV}\) are needed to produce ionization. The effects of x rays and nuclear radiation on biological tissues and other materials, such as solid state electronics, are directly related to the ionization they produce.

All of them, for example, can damage electronics or kill cancer cells. In addition, methods for detecting x rays and nuclear radiation are based on ionization, directly or indirectly. All of them can ionize the air between the plates of a capacitor, for example, causing it to discharge. This is the basis of inexpensive personal radiation monitors, such as pictured in this figure. Apart from \(\alpha \), \(\beta \), and \(\gamma \), there are other forms of nuclear radiation as well, and these also produce ionization with similar effects. We define ionizing radiation as any form of radiation that produces ionization whether nuclear in origin or not, since the effects and detection of the radiation are related to ionization.

The range of radiation is defined to be the distance it can travel through a material. Range is related to several factors, including the energy of the radiation, the material encountered, and the type of radiation (see this figure). The higher the energy, the greater the range, all other factors being the same. This makes good sense, since radiation loses its energy in materials primarily by producing ionization in them, and each ionization of an atom or a molecule requires energy that is removed from the radiation. The amount of ionization is, thus, directly proportional to the energy of the particle of radiation, as is its range.

Radiation can be absorbed or shielded by materials, such as the lead aprons dentists drape on us when taking x rays. Lead is a particularly effective shield compared with other materials, such as plastic or air. How does the range of radiation depend on material? Ionizing radiation interacts best with charged particles in a material. Since electrons have small masses, they most readily absorb the energy of the radiation in collisions. The greater the density of a material and, in particular, the greater the density of electrons within a material, the smaller the range of radiation.

Collisions

Conservation of energy and momentum often results in energy transfer to a less massive object in a collision. This was discussed in detail in Work, Energy, and Energy Resources, for example.

Different types of radiation have different ranges when compared at the same energy and in the same material. Alphas have the shortest range, betas penetrate farther, and gammas have the greatest range. This is directly related to charge and speed of the particle or type of radiation. At a given energy, each \(\alpha \), \(\beta \), or \(\gamma \) will produce the same number of ionizations in a material (each ionization requires a certain amount of energy on average). The more readily the particle produces ionization, the more quickly it will lose its energy. The effect of charge is as follows: The \(\alpha \) has a charge of \(+{2q}_{e}\) , the \(\beta \) has a charge of \(-{q}_{e}\) , and the \(\gamma \) is uncharged. The electromagnetic force exerted by the \(\alpha \) is thus twice as strong as that exerted by the \(\beta \) and it is more likely to produce ionization.

Although chargeless, the \(\gamma \) does interact weakly because it is an electromagnetic wave, but it is less likely to produce ionization in any encounter. More quantitatively, the change in momentum \(\Delta p\) given to a particle in the material is \(\Delta p=F\Delta t\), where \(F\) is the force the \(\alpha \), \(\beta \), or \(\gamma \) exerts over a time \(\Delta t\). The smaller the charge, the smaller is \(F\) and the smaller is the momentum (and energy) lost. Since the speed of alphas is about 5% to 10% of the speed of light, classical (non-relativistic) formulas apply.

The speed at which they travel is the other major factor affecting the range of \(\alpha \) s, \(\beta \) s, and \(\gamma \) s. The faster they move, the less time they spend in the vicinity of an atom or a molecule, and the less likely they are to interact. Since \(\alpha \) s and \(\beta \) s are particles with mass (helium nuclei and electrons, respectively), their energy is kinetic, given classically by \(\cfrac{1}{2}{\text{mv}}^{2}\). The mass of the \(\beta \) particle is thousands of times less than that of the \(\alpha \) s, so that \(\beta \) s must travel much faster than \(\alpha \) s to have the same energy. Since \(\beta \) s move faster (most at relativistic speeds), they have less time to interact than \(\alpha \) s. Gamma rays are photons, which must travel at the speed of light. They are even less likely to interact than a \(\beta \), since they spend even less time near a given atom (and they have no charge). The range of \(\gamma \) s is thus greater than the range of \(\beta \) s.

Alpha radiation from radioactive sources has a range much less than a millimeter of biological tissues, usually not enough to even penetrate the dead layers of our skin. On the other hand, the same \(\alpha \) radiation can penetrate a few centimeters of air, so mere distance from a source prevents \(\alpha \) radiation from reaching us. This makes \(\alpha \) radiation relatively safe for our body compared to \(\beta \) and \(\gamma \) radiation. Typical \(\beta \) radiation can penetrate a few millimeters of tissue or about a meter of air. Beta radiation is thus hazardous even when not ingested. The range of \(\beta \) s in lead is about a millimeter, and so it is easy to store \(\beta \) sources in lead radiation-proof containers.

Gamma rays have a much greater range than either \(\alpha \)s or \(\beta \)s. In fact, if a given thickness of material, like a lead brick, absorbs 90% of the \(\gamma \)s, then a second lead brick will only absorb 90% of what got through the first. Thus, \(\gamma \)s do not have a well-defined range; we can only cut down the amount that gets through. Typically, \(\gamma \)s can penetrate many meters of air, go right through our bodies, and are effectively shielded (that is, reduced in intensity to acceptable levels) by many centimeters of lead. One benefit of \(\gamma \)s is that they can be used as radioactive tracers (see this figure).

PhET Explorations: Beta Decay

Build an atom out of protons, neutrons, and electrons, and see how the element, charge, and mass change. Then play a game to test your ideas!

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