Using Haramein's proton radius equation (the one that predicted the muonic hydrogen proton radius) and the equation we derived in this blog for $\mu={m_p\over m_e}$, we can derived an expression for Avogadro's Constant which is even more accurate than the mainstream value:

$$N_A={A_r(e)M_u\over m_e}$$

$$N_A={{A_r(e)M_u\alpha^2}\over{4\pi\ell m_{\ell}R_\infty}}$$

$$N_A={{A_r(e)M_u\alpha^2}\over{\pi r_pm_pR_\infty}}$$

$A_r(e)=$ electron relative atomic mass

$M_u=$ Molar mass constant

$\alpha=$ fine-structure constant

$m_p=$ mass of proton

$m_e=$ mass of electron

$N_A(new)=6.02214129 \dots \;\;\; \times10^{23}\;per\;mole$

$N_A(old)\;\:=6.022140857(74) \times 10^{23}\;per\;mole$