Cross Section
Definition and meaning of Cross Section in chemistry.
Cross section is a measure of how likely a specific interaction is to happen. It applies to scattering, absorption, or nuclear reactions between a particle beam and a target. It is expressed as an effective area, usually written as sigma.
In more detail
Cross section does not describe the actual physical size of a target particle. Instead, it describes how likely an interaction is for a given number of incoming particles. A larger cross section means a higher chance that an incoming particle will interact with the target.
Scientists define cross section so that the reaction rate equals three things multiplied together. These are the incoming particle flux, the number of target particles per unit volume, and the cross section itself. This links a tiny, microscopic property to reaction rates that can actually be measured in the lab.
Cross sections are not fixed numbers. They change a great deal depending on the energy of the incoming particles. They also depend on which specific process is being studied, such as elastic scattering, absorption, or ionization.
Because of this, a single target material can have many different cross sections. Each one applies to a specific type of interaction and a specific particle energy. Nuclear engineers rely on measured cross sections to predict how a reactor core will behave under different conditions.
Very small cross sections often require intense particle beams or long exposure times to gather enough data. The term cross section is a little misleading. Particles usually behave more like waves than solid spheres in these interactions.
Key facts
| Field | Physical Chemistry |
|---|---|
| Symbol | Sigma |
| SI unit | Square meters, though barns are more commonly used |
| Barn conversion | 1 barn equals 10 to the negative 28 square meters |
| Depends on | Particle energy and the specific type of interaction |
The thermal neutron absorption cross section of boron-10 is about 3,840 barns. This very high value is why boron is used inside nuclear reactor control rods. The boron absorbs neutrons efficiently, helping to control the rate of the fission chain reaction.
Frequently asked questions
Is cross section the same as the physical size of a particle?
No. Cross section is an effective area tied to interaction probability, not a direct measurement of physical size. For simple hard sphere collisions, though, it can roughly match the particle's geometric size.
Why is the barn used as a unit?
The barn equals 10 to the negative 28 square meters, a convenient size since nuclear and atomic cross sections are extremely small in standard SI units. The name came from an old joke that such interactions were as easy to hit as a barn door.
Does cross section change with particle energy?
Yes. The same target can have very different cross sections depending on how much energy the incoming particles carry. This is why cross section values are always reported alongside a specific energy.