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

(i) In electrostatics, `F_(e)=(Kq_(1)q_(2))/r^(2)=(Ke^(2))/r^(2)` ...(1)
where `q_(1)=q_(2)=e`
In gravitation, `F_(g)=(Gm_(1)m_(2))/r^(2)=(Gm_(e)m_(p))/r^(2)` ...(20
Where `m_(1)=m_(e), m_(2)=m_(p)`
`((1))/((2)) implies (Ke^(2))/(G m_(e)m_(p))=F_(e)/F_(g)` ...(3)
Dimensional formula of `(Ke^(2))/(Gm_(e)m_(p))=("Dimensional formula of "F_(e))/("Dimensional formula of "F_(g))`
`=(MLT^(-2))/(MLT^(-2))`
`:.` Dimensions of `(Ke^(2))/(G m_(e)m_(p))=M^(0)L^(0)T^(0)`
Thus the given ratio is dimensionless.
(ii) We known that `e=1.6xx10^(-19) C, G=6.67xx10^(-11)N-m^(2)//kg^(2)`
`m_(e)=9.1xx10^(-31) kg, m_(p)=1.67xx10^(-27) kg, K=1/(4pi epsi_(0))=9xx10^() N-m^(2) c^(-2)`
The value of `(Ke^(2))/(Gm_(e)m_(p))=(9xx10^(9)xx(1.6xx10^(-19))^(2))/(6.67xx10^(-11)xx9.1xx10^(-31)xx1.67xx10^(-27))`
`implies (F_(e))/F_(g)=2.29xx10^(39)` [`:'` from (3)]
`:. F_(e)=2.29xx10^(39) F_(g)`