00:01
In this question, we're looking at neutrons with a kinetic energy of 25 mega electron bolts which are being used in fast neutron therapy.
00:08
We know that they decay with an average lifetime of 886 seconds.
00:13
We want to calculate the lifetime as measured in the laboratory of these neutrons.
00:18
So what we'll do is start by creating an expression for the relativistic kinetic energy.
00:23
It's given by gamma mc squared minus mc squared.
00:35
And what we can do is we can say that the rest energy, so er, is equal to mc squared.
00:43
So we can further equate this to gamma minus one mc squared, which is equal to gamma minus one er.
00:57
And what we can do now is plug in for gamma.
01:01
So we can say that k is equal to one over the square root of 1 minus v squared over c squared minus 1 er.
01:21
So now we've got this, we can rearrange the expression to get it in terms of v.
01:27
Doing this, we get an expression that says that v is equal to the square root of 1 minus 1 over 1 plus k over er squared...