If you see the expression of gravitational force:

$$F=G\frac{m_1m_2}{r^2}$$

it has a coefficient, two mass terms and one distance term.

Now,
$G$ (gravitational constant) $\approx 6.6x10^{-11}$ SI Units
$m_1$ & $m_2$ (suppose mass of an electron) $\approx 9.1x10^{-31}\ \mathrm{kg}$
$r$ (distance between two electrons) $\approx 10^{-12}\ \mathrm m$

Gives us force in range of $10^{-47} - 10^{-46}\ \mathrm N$ which is very very less.

And there are other forces working at those distances like Electrostatic Forces, which have magnitude of $1 - 10\ \mathrm N$

Because gravity is dependent on mass at atomic level where mass of atoms and particle become very little magnitude of gravity also becomes very little. Thats why at atomic level gravity has such insignificant effect.

If you see the expression of gravitational force:

$$F=G\frac{m_1m_2}{r^2}$$

it has a coefficient, two mass terms and one distance term.

Now,
$G$ (gravitational constant) $\approx 6.6\times10^{-11}$ SI Units
$m_1$ & $m_2$ (suppose mass of an electron) $\approx 9.1\times10^{-31}\ \mathrm{kg}$
$r$ (distance between two electrons) $\approx 10^{-12}\ \mathrm m$

Gives us force in range of $10^{-47} - 10^{-46}\ \mathrm N$ which is very very less.

And there are other forces working at those distances like Electrostatic Forces, which have magnitude of $1 - 10\ \mathrm N$

Because gravity is dependent on mass at atomic level where mass of atoms and particle become very little magnitude of gravity also becomes very little. Thats why at atomic level gravity has such insignificant effect.

If you see the expression of gravitational force:

[![enter image description here][1]][1]
it has a coefficient, two mass terms and one distance term.

Now,

  G (gravitational constant) ~ 6.6x10^-11 SI Units
  m₁ & m₂ (suppose mass of an electron) ~ 9.1x10^-31 kg
r (distance between two electrons) ~ 10^-12 m
Gives us force in range of 10^-47 - 10^-46 N
which is very very less.

And there are other forces working at those distances like Electrostatic Forces, which have magnitude of 1 - 10 N

Because gravity is dependent on mass at atomic level where mass of atoms and particle become very little magnitude of gravity also becomes very little. Thats why at atomic level gravity has such insignificant effect. [1]: https://i.sstatic.net/oUwk3.png

If you see the expression of gravitational force:

$$F=G\frac{m_1m_2}{r^2}$$

it has a coefficient, two mass terms and one distance term.

Now, 
$G$ (gravitational constant) $\approx 6.6x10^{-11}$ SI Units 
$m_1$ & $m_2$ (suppose mass of an electron) $\approx 9.1x10^{-31}\ \mathrm{kg}$
$r$ (distance between two electrons) $\approx 10^{-12}\ \mathrm m$

Gives us force in range of $10^{-47} - 10^{-46}\ \mathrm N$ which is very very less.

And there are other forces working at those distances like Electrostatic Forces, which have magnitude of $1 - 10\ \mathrm N$

Because gravity is dependent on mass at atomic level where mass of atoms and particle become very little magnitude of gravity also becomes very little. Thats why at atomic level gravity has such insignificant effect.