Question

Check that the ratio `ke^(2)//Gm_(e) m_(p)` is dimenionless, Look up a table of Physical Constants and determine the value of thisi ratio. What does the ratio signigy ?

Answer 1

`(ke^(2))/(G m_(e) m_(p)) = ([N m^(2) C^(-2)] [C^(2)])/([N m^(2) kg^(-2)] [kg] [kg]) = 1 = (M^(@) L^(@)T^(@))` `:.` The given ratio dimenesionless.
using `k = 9xx10^(9) N m^(2) C^(-2), e = 1.6xx10^(-19)C, G = 6.67xx10^(-11) N m^(2) kg^(-2)`,
`m_(e) = 9.1xx10^(-31) kg, and m_(p) = 1.66xx10^(-27) kg`, we get , `(ke^(2))/(G m_(e) m_(p)) = 2.29xx10^(39)`
This is the ratio of electrostatic force to gravitational force between an electron and a proton.