00:01
In this problem, we're going to talk about relativistic energy.
00:04
And all you need to remember is that the energy of a relativistic particle is equal to mc squared times gamma, where gamma is 1 over the square root of 1 minus v squared over c squared, and v is the speed of the particle.
00:29
And our goal in this exercise is to find what is the speed of some particles given their energy.
00:39
And some things that we're going to need to remember in question a, we're going to need to remember that the mass of the proton is equal to 938 .3m .3 p .113 megallectron volts per c squared.
00:54
And in question b, we're going to need to remember that the mass of the electron is 0 .511 megaelectrum volts per c squared.
01:12
Okay, so notice that if we have the energy, then since the energy is mc squared times gamma, and gamma is 1 over the square of 1 minus v squared over c squared, we can isolate v in this way.
01:34
So 1 minus v squared over c squared is equal to m2.
01:38
X squared over e squared so 1 minus mc squared over e squared if we take the square root of this this is equal to and multiply it by c this is equal to v so now we want to calculate v in this case when e is equal to 500 giga electron volts this is the same as 5 times cent of the fifth meg -electron volts...