# Photon temperature at nucleosynthesis

I've been asked about photon temperature at nucleosynthesis (3 minutes from Big Bang). So I guessed this is the moment when Matter and Radiation where in equilibrium:

$$\rho_M(T) = \rho_R(T)$$

Taking $$\rho_{R,0} = 7.8 \cdot 10^{-34} g/cm^3$$ and $$\Omega_R = \frac{\rho_{R,0}}{\rho_{C,0}} = 4.5 \cdot 10^{-5} h^{-2}$$:

$$1 = \frac{\rho_{R}}{\rho_{M}} = \frac{\rho_{R,0}}{\rho_{M,0}} \frac{a_0}{a} = \frac{\rho_{R,0}}{\rho_{M,0}} \frac{T}{T_0}$$

Then:

$$T = 0.85 eV$$

Is it right?