Final answer:
The question involves calculating the longest wavelength of light emitted in a transition from an excited state to a lower energy one, using the Rydberg formula for hydrogen.
Step-by-step explanation:
The question asks about the longest wavelength of light that can be emitted by a hydrogen atom transitioning from an excited state to a lower energy level. Specifically, it refers to an initial configuration of '60',' which appears to be a typo and might actually mean the n=6 energy level. Electrons in hydrogen can drop from higher excited states to lower ones, emitting light of specific wavelengths in the process. These wavelengths are defined by the Rydberg formula for hydrogen:
\( \frac{1}{\lambda} = R_H \left(\frac{1}{n_{\text{lower}}^2} - \frac{1}{n_{\text{upper}}^2}\right) \\
Where \(R_H\) is the Rydberg constant for hydrogen (\(1.097 \times 10^7 m^{-1}\)), \(n_{\text{lower}}\) and \(n_{\text{upper}}\) are the principal quantum numbers of the lower and upper energy levels, respectively, and \(\lambda\) is the wavelength in meters. For the longest wavelength, the electron would transition from the 6th excited level to the immediately lower energy level, n=5. Solving for \(\lambda\) gives you the wavelength in meters, which can be converted to nanometers (nm).