For which of the following transitions would a hydrogen atom absorb a photon with the longest wavelength? a. n = 1 to n = 2
b. n = 3 to n = 2
c. n = 5 to n = 6
d. n = 7 to n = 6

Hence among the options a and c, option d is that the correct answer because it has rock bottom energy ( as n value increases, energy decreases as energy levels come closer).

Explanation:

The relation between energy and wavelength is:

From this equation, it's clear that wavelength and energy are inversely proportional to every other. The Lower the energy of a specific transition, the longest will the wavelength be of that specific transition.  

Among the given options, options b and d are often ruled out, since those transitions produce to release of a photon because it is coming down from an excited state.

put the answers   and i could answer.