Chech that the ratio `ke^(2)//"G m"_(e)m_(p)` is dimensionless. Look up a table of Physical Constants and setermine the value of this ratio. What does the ratio signify?

Explanation

The electric force acting between an electron and a proton is : `F_"el"=(ke^2)/r^2`
The gravitational force acting between an electron and a proton is : `F_"gr"=(Gm_em_p)/r^2`
The ratio of the electric force to the gravitational force is
`F_"el"/F_"gr"-((ke^2)/r^2)/((Gm_em_p)/r^2)=(ke^2)/(Gm_em_p)`
We can see that the given factor is the ratio of the electric and gravitational forces between an electron and a proton . This is dimensionless entity .
`F_"el"/F_"gr"=((9xx10^9)xx(1.6xx10^(-19))^2)/((6.67xx10^(-11))(9.1xx10^(-31))(1.67xx10^(-27)))`
`=2.27xx10^39`