1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Estimating Neutrino Flux Density

  1. Apr 28, 2013 #1
    1. Problem

    "Estimate the flux of neutrinos passing through your body per second if the present energy density of neutrinos from the Big Bang is 0.2 MeV/m3. Assume that you are a standard size covering 0.01 m2".

    2. Relevant equations

    nv = Uv(T) / <Ev>

    3. The attempt at a solution

    I've assumed that the neutrinos have a temperature of 1.95 K. Now I'm not sure whether to presume that the neutrinos are relativistic (hence, zero mass and velocity of c) or non-relativistic (i.e. mv < 1 eV), since the question does not specify. Although I believe the Tv = 1.95 K value comes from assuming neutrinos are massless (I think).

    I've attempted both and have different answers (although I doubt whether they are correct). Regardless, I've not had much success converting the neutrino density to a flux density. I assume that the neutrinos are travelling in all directions with the same velocity.
    Last edited: Apr 28, 2013
  2. jcsd
  3. Apr 28, 2013 #2


    User Avatar
    2017 Award

    Staff: Mentor

    You can assume that the neutrinos are ultra-relativistic, I think.

    A human body with 0.01m^2 surface area is... strange.
  4. Apr 29, 2013 #3
    I thought that 0.01 m2 was quite low, too. Perhaps he meant 0.1 m2.

    Assuming the neutrinos are ultra-relativistic I got a flux of 1.19 x 1017 m-2 s-1... which I'm pretty sure is higher than the solar neutrino flux. o_O

    I used:

    Flux ϕ = (c . uv(T)) / (3 . <Ev>) = (c . uv(T)) / (3 . kB . T)

    The factor of 1/3 comes from assuming the neutrinos are isotropic. Essentially, this is the power density (which is c/3 times the radiation pressure uv(T)) divided by the average energy of a neutrino <Ev>.

    Do you think this is correct?
    Last edited: Apr 29, 2013
  5. Apr 29, 2013 #4


    User Avatar
    2017 Award

    Staff: Mentor

    Flux should be something "per time*area".

    2K correspond to about .5meV, therefore we have ρ=0.4*10^9 primordial neutrinos per m^2, moving at nearly the speed of light. Using only one direction, the flux is 1/2 ρ c or about 10^17/(m^2*s).
    Looks good.

    Those neutrinos are hard (or even impossible) to detect as they have a very low energy.
  6. Apr 29, 2013 #5
    Ah yeah. Sorry I meant neutrinos per meter squared per second - I'll edit my post.

    Thanks for your reply. Is it appropriate to assume the neutrinos are travelling at a velocity of c and are massless? I thought that when neutrinos decoupled (2s after the Big Bang) they had a velocity close to c, but have since slowed to approximately 105 - 106 m s-1?
  7. Apr 29, 2013 #6


    User Avatar
    2017 Award

    Staff: Mentor

    If they are slow, they are not relativistic - with 2K, they would need some significant mass to be so slow.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted