extension
Relativity model 4 ext b
One of the most famous equations in physics comes out of Einstein's theory of relativity. It is:

 

E=mc2
E stands for energy
m is mass
c is the speed of light

 

But what does it mean and how does it come about?

The ultimate speed
Albert Einstein developed the theory of relativity to explain the way in which light behaves. He stated that nothing can travel faster than the speed of light. Anything that has mass can never actually reach the speed of light. This means that a particle gets more and more difficult to accelerate as it approaches the speed of light.

We call its resistance to acceleration its inertia. A particle with a bigger inertia has a bigger mass. Einstein showed that, in order to prevent the particle reaching the speed of light, it gains mass equal to its total energy divided by the speed of light squared. So:

   m=E÷c2

=> E=mc2

Changing mass
The mass of a system changes if its total internal energy changes - whether it is through binding (like the binding energy of a nucleus) or through travelling extremely fast. In either case, there has not been a transmutation of matter into energy - the total number of particles has remained the same each time. However, although it is a different process, the equation can also predict what happens when matter does change into energy.
Matter into energy
Animation of electron positron annihilation
When a particle of matter meets its anti-particle, they annihilate one another and release energy. The amount of energy they release can be found from Einstein's equation by putting in the total mass of the two particles.

For example, if an electron and positron meet, the energy released will be:

E = mc2
  = 2 x 9.11 x 10-31 x (3 x 108)2
  = 1.6 x 10-13 joules

This is 100, 000 times more than the energy released when two molecules of hydrogen combine with a molecule of oxygen to form water. The energy will be carried off as high-frequency gamma radiation.

Stranger consequences
Sometimes, the reverse can happen. A system that has an extremely high internal energy can spontaneously create a particle and antiparticle. The masses of the particles can be found from the total energy using Einstein's equation. This is used by physicists who are trying to make new particles in accelerators.
The story so far
If the total energy of a system increases, its mass will increase as well
If a particle and antiparticle annihilate each other, they release energy that is equal to their combined mass multiplied by the square of the speed of light
Question M9

a) About how much more energy is released by nuclear changes than by chemical ones?

b) When 1g of hydrogen burns, it releases about 500 kJ of energy. About how much energy would be released if 1g of electrons met with 1g of positrons (anti-electrons)?

c) Where on Earth does this happen?

The story so far
  • There are two families of fundamental particle: quarks and leptons
  • There is antimatter as well as matter
  • Electrons are fundamental particles - part of the lepton family
  • Particles and anti-particles annihilate each other, releasing energy as gamma radiation