Q. 34.2( 96 Votes )

# 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?

Answer :

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 = Nm^{2}kg^{-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 Nm^{2} 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. M^{0} L^{0} T^{0}

Let us now calculate the value of the given ratio,

G = 6.67 × 10^{11} Nm^{2} Kg^{-2}

e = 1.6 × 10^{19} 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 10 ^{39} times greater than the gravitational force.__

Rate this question :