Calculating Energy Levels and Wavelengths in the Hydrogen Atom

[Kennedy111]

Homework Statement

In the hydrogen atom, the electron jumps from the n = 1 level to the n = 4 level.
a. During this transition from n = 1 to n = 4, is a photon emitted or absorbed?
b. What is the change in energy of the electron?
c. State the transition in words.
d. What is the wavelength of the emitted or absorbed photon?

Energy when n = 1 : -13.6 eV
Energy when n = 4 : -0.85 eV

Homework Equations

ΔE = Ef - Ei
λ = hc/E

The Attempt at a Solution

a. I believe I understand this question. I would say that the photon is absorbed...
b. ΔE = Ef - Ei
ΔE = (-0.85 eV) - (-13.6 eV)
= 12.75 eV
c. The electron has made a transition from the n = 1 to the n = 4 energy level.. is that it?? I feel like this question was too easy...
d. I used λ = hv/E but I'm not sure if that was the right formula to use...
λ = (4.14 x 10^-15 eV*s)(3.00 x 10^8 m/s) / (12.75 eV)
= 9.74 x 10^-8 m

I am just unsure of my work and would really like a second opinion. Thank you!

 

[Saitama]

To simplify the calculations in d, you can equate hc=1240 eV nm. Rest everything seems ok to me. (I haven't checked your calculations.)