What is the wavelength in meters of the photon emitted when this highly excited hydrogen atom of hydrogen make

Question

What is the wavelength in meters of the photon emitted when this highly excited hydrogen atom of hydrogen makes its transition from the n = 9 to the n = 8 state?

Answer 1

Without considering the fine structure, the electron energy level of the hydrogen atom can be written as:
En = -2.179×10^-18 J/ n^2
E8 = -3.405×10^-20 J
E9 = -2.690×10^-20 J
Hence E9 - E8 = 7.14×10^-21 J
To convert energy to frequency or wavelength, we have to use the following formula:
E = h•ν = h•c/λ, or λ = h•c/E
where h the Plank constant 6.626x10^-34 J•s, ν the frequency in 1/s, c the speed of light 2.998x10^8m/s, and λ the wavelength in m.
Hence λ = (6.626x10^-34 J•s)*(2.998x10^8m/s)/(7.14×10^-21 J)
= 2.78x10^-5 m.