Question

For Fe25+ ion, calculate the wavelength of the light that is emitted upon the electron's transition from n=4 to n=3.

Answer 1

Your energy equation agrees with the ref. 1 link.
Let B = Bohr level-1 energy constant = 2.180E-18 J
Δenergy = BZ^2*(1/N1^2-1/N2^2) = 2.180E-18*25^2*(1/9-1/16) = 6.622875E-17 J
lambda = hc/Δenergy = 2.99937E-9 m
EDIT: Note that B = hc*Rydberg constant. That explains the agreement between Al's (revised) and my answers. What I called B is actually the Rydberg energy (as distinct from the Rydberg constant). I'm learning as I go.
Also note that the powers that be have updated the values of h and "B" (from ref. 2):
h = 6.62606896E-34 J-s
B = 2.17987197E-18 J