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What is Elastic Scattering?

Alex Paul
Alex Paul

Elastic scattering occurs when two or more particles collide without any loss of energy. This means that while the directions of the particles may change, the total kinetic energy of the system, or movement energy, is always conserved. The term elastic scattering is typically used in particle physics, which is the study of microscopic particles, but an elastic collision can also take place between macroscopic objects. An inelastic collision occurs when energy is lost during the collision.

The term elastic scattering comes from scattering theory, which is a set of rules and equations which describe how particles and waves interact. In the macroscopic world, when two objects collide it is usually through a physical collision. In particle physics, however, the objects may collide through other forces, including electromagnetic collisions. An elastic collision can occur between any objects and in any type of collision.

The collison of billiard balls shows elastic scattering.
The collison of billiard balls shows elastic scattering.

Elastic scattering is very important in particle physics. When electrons collide with other particles, for example, the collision is elastic as no energy is lost. This is known as Rutherford scattering and is a phenomenon that led to the discovery of the structure of the atom.

In the macroscopic or physical world, it is exceptionally unlikely for a true elastic collision to occur between two large objects. This is due to surrounding forces as well as the vibrations that occur inside large objects. There are some situations, however, where a collision can be approximated as elastic. This is useful as it allows for the predicted speed and direction of two objects after a collision to be estimated using simpler methods.

An example of elastic scattering can be seen in games of snooker or pool.
An example of elastic scattering can be seen in games of snooker or pool.

A common example of elastic scattering in the physical world is the collision of two billiard balls. Although a small amount of energy will be lost in this collision due to friction, this is small enough to be negligible. When two billiard balls collide, the second ball gains almost exactly the amount of energy that the first ball loses, so the total kinetic energy of the system is conserved.

Inelastic scattering occurs when the total energy of the two or more colliding objects is not conserved. In collisions between real world objects, inelastic collisions are much more common. This is mainly due to the extra vibrations which will occur when a large object collides with another, as these vibrations take up energy that would have been used for movement. Momentum, however, is always conserved in both elastic and inelastic collisions.

Discussion Comments


@Charred - Billiards is one thing, but small particles are another. Light scattering by small particles would seem to result in a somewhat random occurrence, you would think at first.

But in my college physics course we discovered that they had their own set of formulas just as you did for large scale objects.

It has applications in a variety of industries. I remember watching this big budget Hollywood animated movie once where most of the action took place in the ocean.

The animated spectral colors and refraction from the light were incredibly realistic, no doubt because they followed the same formulas as used for real life light scattering.


I well remember studying elastic and inelastic collisions in physics – the billiard ball being the prime example.

We had to do these formulas with mass and velocity. Given the correct values, you could predict the velocity of the second object as it received impact from the first object. There would be an immediate transfer of momentum from the first object to the second.

I always loved physics examples that used billiards. I wondered if I mastered the conceptual principles well enough, if I could someday become a pool shark.

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    • The collison of billiard balls shows elastic scattering.
      By: Marijus
      The collison of billiard balls shows elastic scattering.
    • An example of elastic scattering can be seen in games of snooker or pool.
      By: Ruslan Kokarev
      An example of elastic scattering can be seen in games of snooker or pool.