00:01
So we're asked to work out the uncertainty in the mass of a muon, given its mass m, specified in electron volts per c squared, given its lifetime, which i've called delta t, of 2 .20 microseconds.
00:15
So the way we need to start this question is by considering the uncertainty principle.
00:20
So we know that the uncertainty in the particle's energy is going to be greater than or equal to so planck's constant in its reduced form h -bar over delta t, which we've called the lifetime here.
00:33
We also know that delta e is equal to the change in its rest mass delta m times by the speed of light, c squared.
00:44
So we can sub in the expression for delta e here to get an expression relating the uncertainty in the mass with the uncertainty in the lifetime.
00:54
So delta m multiplied by c squared is greater than or equal to h bar over delta t.
01:01
I've just equated the delta e's here so we can rearrange for delta m and what we're going to do because it wants our units in c square we're just going to simply take that out but dividing by our c squared here so delta m is greater than or equal to and i will just make a little note in one over c squared just to say that we've got the units of one over c squared here so delta m is greater than or equal to at all equal to h bar over delta t...