The energy levels of the hydrogen atom are quantized and their energy is given by the approximated formula
where n is the number of the level.
In the transition from n=2 to n=6, the variation of energy is
Since this variation is positive, it means that the system has gained energy, so it must have absorbed a photon.
The energy of photon absorbed is equal to this
. Converting it into Joule,
The energy of the photon is
where h is the Planck constant while f is its frequency. Writing
, we can write the frequency f of the photon:
The photon travels at the speed of light,
, so its wavelength is
So, the initial sentence can be completed as:
The n = 2 to n = 6 transition in the bohr hydrogen atom corresponds to the "absorption" of a photon with a wavelength of "411" nm.