The Balmer series for the hydrogen atom comprises electron energy transitions that end in the n, = 2 state. ENERGY Balmer series E (eV) 0.00 -0.378 -0.544 2 -0.850 4 -1.512 -3.401 0 Consider the four illustrated transitions, each shown by a downward arrow in this energy-level diagram for the hydrogen atom. Because these transitions all involve a hydrogen atom losing energy, they each correspond to the emission of a photon. (a) What is the initial quantum number, n,, of the transition that generates the photon with the longest wavelength? (Restrict your attention to the four illustrated transitions.) n = 3 (b) What is the energy (in eV) of that longest-wavelength photon? 1.89 ✓ev (c) What is its wavelength (in nm)? 410 You have computed the wavelength for the photon resulting from a transition between n, = 6 and n = 2. Of the four transitions illustrated with downward arrows, is this the most or least energetic? In turn, is this the photon with the shortest or longest wavelength? Are energy and photon wavelength directly or inversely proportional to one another? nm Now consider the transition (out of the four depicted) that generates the photon with the shortest wavelength. (d) What is the initial quantum number, n,, of the transition that generates the photon with the shortest wavelength? (Again, restrict your attention to the four illustrated transitions.) 6 nm (e) What is that photon's energy (in eV)? 3.02 ✔ev (f) What is that photon's wavelength (in nm)? 257 x Only four initial quantum numbers (3, 4, 5, and 6) are under consideration. Of these, which will provide the photon with the longest wavelength? What is the energy difference between that level and ny = 2? From that, how can you compute the wavelength? nm (9) Finally, consider all transitions from n, > 2 that end at n, = 2 (in other words, the entire Balmer sequence, not limited to the four illustrated transitions). What is the shortest possible wavelength (in nm) for any photon picked from the Balmer ser

The Balmer series for the hydrogen atom comprises electron energy transitions that end in the n, = 2 state. ENERGY Balmer series E (eV) 0.00 -0.378 -0.544 2 -0.850 4 -1.512 -3.401 0 Consider the four illustrated transitions, each shown by a downward arrow in this energy-level diagram for the hydrogen atom. Because these transitions all involve a hydrogen atom losing energy, they each correspond to the emission of a photon. (a) What is the initial quantum number, n,, of the transition that generates the photon with the longest wavelength? (Restrict your attention to the four illustrated transitions.) n = 3 (b) What is the energy (in eV) of that longest-wavelength photon? 1.89 ✓ev (c) What is its wavelength (in nm)? 410 You have computed the wavelength for the photon resulting from a transition between n, = 6 and n = 2. Of the four transitions illustrated with downward arrows, is this the most or least energetic? In turn, is this the photon with the shortest or longest wavelength? Are energy and photon wavelength directly or inversely proportional to one another? nm Now consider the transition (out of the four depicted) that generates the photon with the shortest wavelength. (d) What is the initial quantum number, n,, of the transition that generates the photon with the shortest wavelength? (Again, restrict your attention to the four illustrated transitions.) 6 nm (e) What is that photon's energy (in eV)? 3.02 ✔ev (f) What is that photon's wavelength (in nm)? 257 x Only four initial quantum numbers (3, 4, 5, and 6) are under consideration. Of these, which will provide the photon with the longest wavelength? What is the energy difference between that level and ny = 2? From that, how can you compute the wavelength? nm (9) Finally, consider all transitions from n, > 2 that end at n, = 2 (in other words, the entire Balmer sequence, not limited to the four illustrated transitions). What is the shortest possible wavelength (in nm) for any photon picked from the Balmer ser