In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :

Coulomb force:

$$F_e=\frac{1}{4\pi\epsilon_0}\frac{e^2}{r^2}$$

Gravitational force:

$$F_g=\frac{Gm_pm_e}{r^2}$$

Ratio,

$$\frac{F_e}{F_g}=\frac{1}{4\pi\epsilon_0}\frac{e^2}{Gm_pm_e}$$

Using approximate values,

$$\frac{1}{4\pi\epsilon_0}=9\times10^9$$

$$e=1.6\times10^{-19}$$

$$G=6.67\times10^{-11}$$

$$m_p=1.67\times10^{-27}$$

$$m_e=9.1\times10^{-31}$$

Substituting gives order

$$\frac{F_e}{F_g}\sim10^{39}$$

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