0:00
Hi.
00:02
So in this question we have a particle known as a pion which lives for a very short time before breaking apart into other particles.
00:10
We suppose that this pion is moving at a speed very close to the speed of light and an observer who is stationary in the lab measures the pion lifetime as a certain value.
00:22
So 2 .5 times 10 to the minus 8 seconds.
00:25
In the first part of the question we have to determine the lifetime of this pion and according to a hypothetical person who is riding along with the pine.
00:36
So in physics we say that this hypothetical person sits in the reference frame of the pion.
00:43
So in that frame where the pion is stationary.
00:47
So in order to solve this part of the question we have to think about a critical concept in special relativity which is time dilation.
00:59
So time dilation states the following principle.
01:06
So if we have some time measured in the lab, so in the lab frame, this time interval is equal to gamma t0.
01:17
So t0 is measured in the rest frame and gamma here is the relativistic factor or the lawrence factor.
01:31
So this is the principle of time dilation.
01:34
So if the pion leaves for an amount t0 in its own rest frame, with that hypothetical person in the rest frame of the pion, then someone sitting in the lab frame will actually measure a different value t.
01:48
The relativistic factor gamma is always larger or equal to 1.
01:52
So this means that the amount of time t measured by the person in the lab will always be larger, greater or equal to t0, the amount of time measured by the hypothetical person sitting in the rest frame where the pion is stationary.
02:11
So for this question, we actually have to solve for t0, so the value in the rest frame.
02:16
So t0 is t divided by gamma.
02:20
Now, what is gamma? so gamma is actually a factor which is related to the velocity of the particle.
02:28
So gamma is given by 1 over the square root of 1 minus v over c squared.
02:34
So in our case v over c is given by 0 .991.
02:42
So gamma can be calculated from this expression here, 1 divided by the square root of 1 minus 0 .991 squared.
02:52
So if you use a calculator you'll get the value of gamma.
02:56
Right.
02:58
Now to calculate t0, we need to divide t...