Rydberg Equation Exercise \(\PageIndex{1}\) What is the wavelength of light emitted when an electron in a hydrogen atom undergoes a transition from energy level n = 3 to level n = 1? ( c = 3.00 × 10 8 m/s, h = 6.63 × 10 –34 J·s, R H = 2.179 × 10 –18 J) Answer 102 nm \[\frac{hc}{\lambda } = R_{H}\left [(\frac{1}{(n_{1})^{2}})-(\frac{1}{(n_{2})^{2}}) \right ]\] \[\frac{(6.63*10^{-34})(3.00*10^{8})}{\lambda }=(2.179*10^{-18})(\frac{1}{1}-\frac{1}{9})\] \[\lambda = \frac{1.981*10^{-25}}{1.937*10^{-18}}\] \[\lambda = 1.023*10^{-7}\;m\] Exercise \(\PageIndex{2}\) The electron in a hydrogen atom, originally in level n = 5, undergoes a transition to a lower level by emitting a photon of wavelength 1583 nm. What is the final level of the electron? ( c = 3.00 × 10 8 m/s, h = 6.626 × 10 –34 J·s, R H = 2.179 × 10 –18 J) Answer 3 Emission Lines Exercise \(\PageIndex{3}\) If a hydrogen atom in the excited n = 5 state relaxes to the ground state, what is the maximum number of possible emission lines? Answer 15