- Velocity = speed and direction of an object
- If an object is travelling in a circle then it is constantly changing direction.
- It is therefore accelerating so there must be a resultant force acting on it.*
- The force that keeps something moving in a circle is the centripetal force.
*Resultant force = the total force that results from two or more forces acting on a single object.
If the resultant force acting on a body is not zero, it will accelerate in the direction of the resultant force.
- In a cyclotron, a charged particle has a constant magnetic field applied to it.
- This is applied at right angles to the particle's motion (perpendicular) to provide the centripetal force needed for circular motion.
- A potential difference is placed across the gap between two electrodes (dees) to accelerate the particle across.
- The path of the particle spirals outwards as its speed increases. Eventually, it leaves the magnetic field and travels in a straight line towards another particle beam.
Uses of Particle Accelerators
- If a high energy proton is allowed to collide with a stable element, then the nucleus of that element will become an unstable nucleus of a different element.
- The result is a radioactive isotope. The unstable isotope will emit α particles, β particles, γ rays or neutrons.
- Small cyclotrons can be used in hospitals to produce the short lived isotopes needed for PET scanners.
- Scientists can use particle accelerators to observe the radiation given off and to discover new types of particles. This helps scientists develop better explanations of the physical universe.
Momentum and Kinetic Energy
- Colliding objects have kinetic energy and momentum (mass x velocity).
- Momentum is always conserved. It is a vector so it has both size and direction.
- In an elastic collision, KE is also conserved.
- In an inelastic collision, KE is not conserved. It can be dissipated as other forms of energy such as heat or sound.
- When a positron meets an electron, the result is annihilation.
- They approach each other with the same mass but at opposite velocities.They therefore have equal but opposite momentum so the total momentum before collision is 0.
- Gamma rays are produced from annihilation. As momentum is always conserved, the two γ rays need to have a momentum of 0.
- The γ rays have the same energy (which has a mass equivalent) but opposite velocities. The momentum after collision is therefore 0.
- Charge is also conserved. An electron (-1) and a positron (+1) result in a neutral (0) charge. γ rays have no charge so therefore charge is conserved.
Positron emission tomography
- A radio isotope produced by a cyclotron emits positrons.
- The positrons are injected into the blood through a tracer. The tracer accumulates in various bodily tissues.
- After a short distance, the positrons will encounter an electron.
- Electron-positron annihilation will take place, emitting a pair of γ rays.
- The γ rays are detected by sensors positioned around the patient. Their detection allows a picture of the internal organs to be produced.