How do I find the exact value of an expression with physical constants

Question

I want to find the exact value for Rydberg constant, so I Type

N[(1/(4*pi *eO))^2     * ((m *e^4)/((h)^3*c (4 pi)))] ;
Needs[Miscellaneous`PhysicalConstants` ];
values = {e -> ElectronCharge, m -> ElectronMass, 
   eO -> ElectricConstant, h -> PlanckConstantReduced, 
   c -> SpeedOfLight};

and the program shows (0.015625 e^4 m)/(c eO^2 h^3 pi^3).

What should I do in order to find the numerical value.

Answer 1

This is three commands. You discard the output of all of them. What did you expect to happen?

Related: You appear to be using an old version of the software. The PhysicalConstants package was made part of the core language in version 9.0 (November 2012).

In the current version (11.2),

values = {
    e -> Quantity["ElementaryCharge"], 
    m -> Quantity["ElectronMass"], 
    eO -> Quantity["ElectricConstant"], 
    h -> Quantity["ReducedPlanckConstant"], 
    c -> Quantity["SpeedOfLight"]
};

UnitConvert[
    (1/(4*\[Pi]*eO))^2*((m*e^4)/((h)^3*c (4 \[Pi]))) /. 
        values, 
    1/"Meters"
]

(*  Result:
    Quantity[1.097373*10^7, 1/("Meters")]  
*)