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 )
me and mp 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
me = 9.1 × 10-31 kg
mp = 1.66 × 10-27 kg
On substituting these values into the ratio, we get
This implies that the electric force between a proton and an electron is 1039 times greater than the gravitational force.
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