Problem regarding determining mass of neutrino

[dilloncyh]

problem regarding determining mass of neutrino (urgent)

1. Homework Statement [/b]
It is found that the speed v of the neutrinos with 10 MeV of total energy is
(1- v/c) < 2x10^(-9) Estimate the mass of the neutrinos in terms of eV, and determine whether the value you find is an upper or lower limit.

My attempt:

I just start with (mc^2)(gamma) = 10Mev (m is the mass of neutrino, gamma is the Lorentz factor), and get v/c = ((1-((mc^2)/10MeV)^2)^1/2 after doing some algebra. Then, I solve the inequality and get m<632.45 eV. Is my approach and answer correct?

thx

 

[ehild]

Check the magnitudes.

ehild

 

[dilloncyh]

If the question asks for the mass in terms of eV, do I multiply the mass in kg by c^2 then divide by e?

 

[ehild]

No, the mass is needed in eV-s. Have you transformed 10 MeV to eV-s ?

ehild

 

[dilloncyh]

Well, I get m < 1.1259 x 10^-33 kg, is this answer correct?

 

[ehild]

The value you got for the mass in eV-s is wrong. No use to transform it to kg-s. Check your calculations: substitute the energy in eV-s.

ehild

 

[dilloncyh]

But is my approach correct? Express 10MeV in terms of (gamma)mc^2, then find the expression of v/c after some algebra, and solve that inequality to get m.

 

[ehild]

Yes, your approach is correct, but read the text of the problem

" Estimate the mass of the neutrinos in terms of eV, and determine whether the value you find is an upper or lower limit. "

The equation you used (mc²)(gamma) = 10MeV is also correct. The rest mass in eV is just 10⁷/gamma, and v/c is given :1-v/c<2˙10^-9 .

No need to calculate the mass in kg-s.

I checked my calculation, and your result in the first post was correct. Sorry.

ehild