Show that is e is electronic charge, h is Planck's constant, c is velocity of light and in_0 is electirc permittivity of free space, then e^2//"in"_0 hc is dimensionless.

Show that is e is electronic charge, h is Planck's constant, c is velo

1.	Show that is e is electronic charge, h is Planck's constant, c is velocity of light and in_0 is electirc permittivity of free space, then e^2//"in"_0 hc is dimensionless.
Answer» Solution :We know that electrostatic potential energy between two ELECTRONS separted by DISTANCE r `is U = (E e)/(4pi "in"_0r)` `:. Units of (e^2)/("in"_0) = U xr = (ML^2 T^(-2))L` Also, energy of a photon, `E = h v = (hc)/(lambda)` `:. Units of hc = E xx lambda = (ML^2 T^(-2))L` `Now = (e^2)/("in"_0hc) = (ML^2T^(-2))/((ML^2T^(-2))L) = [M^0 L^0 T^(0)]` i.e., the given quantity is dimensionless.