College Chemistry
posted by Bach .
In energy terms, ionization of an electron in an atom corresponds to the transition from whatever quantum state the electron is in to an energy of 0 KJ/mole. Calculate the energy in joules needed to remove one electron in the n=1 state from a hydrogen atom.
I know En of 1 = 1312 KJ/mole
so delta En =  0+1312 = 1312 KJ/mol
1312 KJ/mol x 1mol/6.022 x 10^23 particles x 1000joules/KJ
is this the correct why to approach this problem? Are my steps correct?

Yes but I would have gone about it another way.
1312000/6.022 x 10^23 = 2.18 x 10^18 J/atom by your calculations.
I would use
delta E = 2.180 x 10^18 J (1/N1^2 1/N2^2)
For N2 = infinity, 1/N^2 is zero and 1/N1^2 = 1; therefore, E = 2.180 x 10^18 joules/atom