Check that the ratio is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

The given ratio is

It is the ratio of electric force i.e.to gravitational force i.e.

between a proton and an electron with the distance between them as constant.

This is because

Here, G = Gravitational constant. (Unit = Nm²kg^-2 )

m_e and m_p are the mass of electron and proton respectively. (Unit = Kg)

e = Electric charge (Unit = Coulomb)

K is a constant =

is the permittivity of space. Its units are Nm² C^-2.

Let us substitute the units into the ratio in order to deduce the dimensions,

All the units get cancelled, and we see that the given ratio is dimensionless i.e. M⁰ L⁰ T⁰

Let us now calculate the value of the given ratio,

G = 6.67 × 10¹¹ Nm² Kg^-2

e = 1.6 × 10¹⁹ C

m_e = 9.1 × 10^-31 kg

m_p = 1.66 × 10^-27 kg

On substituting these values into the ratio, we get

Note:

This implies that the electric force between a proton and an electron is 10⁴⁰ times greater than the gravitational force.