Consider the transition from the energy levels n = 3 to n = 6. what is the wavelength associated with this transition, in nm?

In quantum chemistry, when the energy of electron changes by moving from orbital to orbital, it emits or absorbs energy in the form of light. When this happens, you can measure its wavelength. Suppose an atom is heated. This excites the electron so it moves up higher to the next orbital. As a result, it would emit light. When its energy lowers and moves one orbital lower, it would absorb light. The equation to determine the wavelength is called the Rydberg formula.

1/wavelength = R(1/n1^2 - 1/n2^2), where
R is an empirical constant called Rydberg's constant equal to 1.9074 × 10^7 m^-1
n1 and n2 are orbitals of the atoms such that n2 is always greater than n1.

Substituting the values:

1/wavelength = 1.9074 × 10^7 (1/3^2 - 1/6^2)
wavelength = 1.09 × 10^-6 m or 1.09 micrometers