Like this?

r = 1.09710^7;
h = 6.6260710^-34;
ev = 1.60217663410^-19;
c = 2.9979245810^8;
rh = 13.6;

Manipulate[
 wL = 1/(r ((1/m^2) - (1/n^2))) 10^9;
 en = -rh ((1/n^2));
 {wL, en},
 {m, 1, 9}, {n, 2, 9}]

Dear Hans,

what if I want to use one of the inputs of a calculation in Manipulate to express the energy?

Energy (in eV) of an orbital:

E = -Rh (1/n^2)

that would be :

Manipulate[-rh*((1/n^2)), {n, 1, 9, 1}]

But what I have in mind is to have a Manipulate that has an output of the wavelength, the different energy, and use that input of n to calculate the energy as above.

Likewise, I wanted to explore the use of the output from the calculation in Manipulate and come out with some other calculation, inside the Manipulate itself.

I am asking these questions because the ref. documentation only holds very simple examples.

Many thanks in advance! Mauro B.

Or maybe something along these lines?

Manipulate[
    x = a*b;
    z = x^c;
    Grid[{
        {"Product of a and b", x},
        {"The product raised to c", z}
    },
     Alignment -> {{Left, Right}, Automatic}, Spacings -> 2
    ],
    {{a, 2}, 0, 10, 1, Appearance -> "Labeled"},
    {{b, 3}, 0, 10, 1, Appearance -> "Labeled"},
    {{c, 4}, 0, 10, 1, Appearance -> "Labeled"},
    {x, None},
    {z, None}
 ]