Cross Section
Definition and meaning of Cross Section in chemistry.
Cross section is a measure of the probability that a specific interaction, such as scattering, absorption, or a nuclear reaction, will occur between a particle beam (photons, electrons, neutrons, or other particles) and a target, expressed as an effective area."
In more detail
The cross section, usually denoted σ, does not correspond to the physical geometric size of the target particle but instead quantifies interaction likelihood: a larger σ means a higher probability of interaction for a given flux of incoming particles. It is defined so that the reaction rate equals the incident particle flux times the target number density times σ, linking a microscopic quantity to macroscopic, measurable rates. Cross sections depend strongly on the energy of the incoming particles and the specific process involved (elastic scattering, absorption, ionization, etc.), so a single target can have many different cross sections for different reactions and energies.
Key facts
| Symbol | σ (sigma) |
|---|---|
| SI Unit | square meter (m²); commonly expressed in barns (1 barn = 10⁻²⁸ m²) |
| Field | Physical Chemistry |
| Depends On | Particle energy and the specific interaction type (scattering, absorption, reaction) |
The thermal neutron absorption cross section of boron-10 is about 3,840 barns, which is why boron is used in nuclear reactor control rods to absorb neutrons and regulate 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 related to interaction probability, not a direct measurement of physical dimensions, though for hard-sphere collisions it can approximate geometric size.
Why is the barn used as a unit?
The barn (10⁻²⁸ m²) is convenient because nuclear and atomic cross sections are extremely small in SI units; it was named because such interactions were, informally, 'as easy to hit as a barn' compared to expectations at the time.