# Lets try solving this

1. Jun 25, 2005

### panthera

hi,

I have a problem and I am trying it out and would like to have suggestions as well. I would post the solution after I finish and will have opinions .Meanwhile I would like others to try this....I shall be obliged to get any ans...

An unstable particle of rest energy 1000MeV decays into a meu-meson (Mo csqr=100MeV) and a neutrino with a mean life, when at rest, of 10^-8 sec.
a) calculate the mean decay distance when the particle has a momentum of 1000MeV/c.
b) What is the energy of the meu-meson if it is emitted at an angle 15 degrees.

ps- i guess its the spelling of meu as i can't write the symbol,correct if it's wrong...
and ^ stands for "raised to the power"
Thanks

2. Jun 25, 2005

### OlderDan

I have an answer for a) as the product of the particle velocity times its time-dilated mean life. The velocity is found from the initial momentum and rest energy. Have you found this?

I'm working on b)

3. Jun 25, 2005

### panthera

thanks...yes i have found a) in the same way...and have got the ans 3m...

for 2nd one i am using four vectors......i always face difficulty in solving these problems using other methods...its almost solved but i hav not yet put the values to get the ans...

4. Jun 26, 2005

### panthera

four vectors----

Px =( Px, jEx)

P μ =(Pμ ,jEμ)

P ν =( P ν , jE ν)

[I tried to put arrow head but couldn't, its getting displaced]

Now,

P ν = Px - P μ

Squaring we get

P ν 2 = (Px - P μ) 2

=>mx2 + mμ2 – 2Ex E μ + 2Px P μ cos θ = 0, θ = 15 degrees

by putting values and neglecting mμ2 we get

E μ =1115.36 MeV [here, E μ is equivalent to P μ ]

is this correct?

Last edited: Jun 26, 2005
5. Jun 26, 2005

### OlderDan

Deleted erroneous calculations and related comments

Last edited: Jun 26, 2005
6. Jun 26, 2005

### panthera

thanks for the solution ...well i am not finding any sign error in my equation; its by solving 4 vectors... only i have multiplied the original eqn with -1 to write it in simplified way[i have not written all the steps here]....your equations are correct but i think we have a sign mismatch.. ...i generally avoid the term mμ sqr in such problems as in case of high energy muons, its negligible....

thanks

Last edited: Jun 26, 2005
7. Jun 26, 2005

### OlderDan

I did make an error, but it was worse than just a sign mistake. I now agree with your original equation, but my earlier result is way off. I have reproduced your result neglecting the rest mass of the muon. Without the approximation, it's a messy thing to be sure.

Last edited: Jun 26, 2005
8. Jun 26, 2005

### panthera

thanks for your suggestions and cooperation..okay...so i can infer that my ans is correct

thanks & regards

Last edited: Jun 26, 2005
9. Jun 26, 2005

### OlderDan

Yep.. looks good to me now. I even managed to get through it without neglecting the muon rest mass. I thought it might be useful to have the general result in hand I got 1116.84Mev. Obviously not a big dfference for this problem.

10. Jun 27, 2005

### panthera

by NOT neglecting, i got somewhat similar results as yours...

cheers

Last edited: Jun 27, 2005