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Arman777

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## Homework Statement:

- What mass would a neutrino need to still be relativistic today (T = 2.37K) ?

## Homework Equations:

- ##T_{\nu} = T_{\gamma}/1.40##

I came across a question that states

So for a particle to be relativistic we need ##pc \gg mc^2##

Well Neutrino was relativistic in the early universe, so I took the time when the neutrino decoupled which is approximately ##\approx 1 MeV##

So I did something like

$$\frac{E_{now}}{E_{dec}} = \frac{kT_{now}}{T_{dec}} = \frac{8.617\times 10^{-5} eV K^{-1} \times 2.73K}{1Mev} = 2.3 \times 10^{-10}$$

But I am kind of stuck here since we need some value for the neutrino mass I guess ? Or my approach is completely wrong (?)

In general, how can we solve this kind of problem? What makes the transition from Non-Relativistic to the relativistic case? The temperature of the universe right..? For instance when the temperature of the universe was larger than the ##1 MeV## we would call protons relativistic

**What mass would a neutrino need to still be relativistic today (T = 2.37K) ?**So for a particle to be relativistic we need ##pc \gg mc^2##

Well Neutrino was relativistic in the early universe, so I took the time when the neutrino decoupled which is approximately ##\approx 1 MeV##

So I did something like

$$\frac{E_{now}}{E_{dec}} = \frac{kT_{now}}{T_{dec}} = \frac{8.617\times 10^{-5} eV K^{-1} \times 2.73K}{1Mev} = 2.3 \times 10^{-10}$$

But I am kind of stuck here since we need some value for the neutrino mass I guess ? Or my approach is completely wrong (?)

In general, how can we solve this kind of problem? What makes the transition from Non-Relativistic to the relativistic case? The temperature of the universe right..? For instance when the temperature of the universe was larger than the ##1 MeV## we would call protons relativistic

**[Moderator's note: Moved from a technical forum and thus no template.]**
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