# How long does a moun live during a measurement

1. Sep 5, 2012

### DODGEVIPER13

1. The problem statement, all variables and given/known data
A muon with a kinetic energy of 200 ± 0.05 MeV
is produced in a linear accelerator. The rest
mass of the muon is 106 MeV/c2.
(a) Calculate the speed of the muon (in units of c),
(b) Calculate the linear momentum (in units of eV/c),
(c) How long does it live during the measurement?
(d) Find the lifetime of the muon.
(e) What is the distance traveled by muon in laboratory
before it disappears (use c = 3 x 108 m/s)? Could
this distance be measured?
(f) For identifying a muon what method do you think
that is better: (1) based on measurements of energy
or (2) based on measurements of distance? Why?

I am having trouble with part c

2. Relevant equations
(1 stands for naught)
E = E1 + K
deltaE dot deltaT = h (I dont understand this equation)
deltaT = h/deltaE

3. The attempt at a solution
I found this and the solution online I understand part a and b then answers are respectivley v=.938c and p=287MeV/c. It is part c that im struggling with this is what my instructor does he says deltaE dot deltaT = h which isnt on my equation sheet so im not sure about this. Then he states E = K + E1 remains constant, then sets deltaE=deltaK = .1MeV I think I understand where he got the equality part and I think I get how he got .1 I assume he did this .05-(-.05) = .1 = deltaK = deltaE. But I am not sure as to why he did this. Then deltaT = h/deltaE = (6.58e-16 eV.s)/(1e5 eV) = 6.58e-21s. How the heck did he obtain 6.58e-16 I am confused?

2. Sep 6, 2012

### DODGEVIPER13

Ouch! no replies yet very weird I guess maybe I was confusing or something.

3. Sep 6, 2012

### voko

The equation you don't understand seems to be the uncertainty principle for energy and time.

4. Sep 6, 2012

### DODGEVIPER13

lol after looking up the uncertainty principle I agree thats what it is but I really need to know where the .1 and 6.58e-16 came from?

5. Sep 7, 2012

### voko

.1 comes from the uncertainty of energy. 6.58e-16 is Planck's constant in eV.s.