I will like to know what I am doing wrong in calculating the energy difference when there is a transition of n=3 to n=2 for 1 mol of hydrogen atoms because I keep on getting 1.82*10^(5). Thanks
For each atom, the energy change is 13.6 eV * (-1/9 + 1/4) = 1.889 eV
1 eV = 1.602*10^-16 J so that energy is
3.03*10^-19 J. Multiply that by Avogadros's number for the energy per mole. I agree with your number.