An electron falling from one energy level to another emits a photon of wavelength 550nm. What is the difference between the two energy levels?

The key equation is that of the energy of a photon.

E = hc/λ​ 

Using λ​ = 550nm gives E = 3.61x10^-19J (Remember that a nanometer is 1x10^-9 m).

Using the conservation of energy, the energy of this photon must be the energy lost by the electron.

Hence, the energy gap E = 3.61x10^-19J