The Balmer series for the hydrogen atom comprises electron energy transitions that end in the nf = 2 state. An illustration of energy levels shows the colors of the lines of the Balmer series. The bottom energy level in the diagram is n = 2, and an upward arrow indicates that energy increases with higher energy levels, labeled up to n = ∞, where E = 0.00 eV. The energy of n = 2 is −3.401 eV, n = 3 is −1.512 eV, n = 4 is −0.8504 eV, n = 5 is −0.5442 eV, and n = 6 is −0.378 eV. Balmer lines are produced when an electron jumps to n = 2 from any higher level. Red color is emitted during transition from n = 3, green color during transition from n = 4, blue color during transition from n = 5, and violet color during transition from n = 6. 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, ni,of the transition that generates the photon with the longest wavelength? (Restrict your attention to the four illustrated transitions.) ni = (b)What is the energy (in eV) of that longest-wavelength photon? eV (c)What is its wavelength (in nm)? 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, ni,of the transition that generates the photon with the shortest wavelength? (Again, restrict your attention to the four illustrated transitions.) (e)What is that photon's energy (in eV)? ?eV (f)What is that photon's wavelength (in nm)? ? nm (g)Finally, consider all transitions from ni > 2 that end at nf = 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 series? ?nm

The Balmer series for the hydrogen atom comprises electron energy transitions that end in the nf = 2 state. An illustration of energy levels shows the colors of the lines of the Balmer series. The bottom energy level in the diagram is n = 2, and an upward arrow indicates that energy increases with higher energy levels, labeled up to n = ∞, where E = 0.00 eV. The energy of n = 2 is −3.401 eV, n = 3 is −1.512 eV, n = 4 is −0.8504 eV, n = 5 is −0.5442 eV, and n = 6 is −0.378 eV. Balmer lines are produced when an electron jumps to n = 2 from any higher level. Red color is emitted during transition from n = 3, green color during transition from n = 4, blue color during transition from n = 5, and violet color during transition from n = 6. 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, ni,of the transition that generates the photon with the longest wavelength? (Restrict your attention to the four illustrated transitions.) ni = (b)What is the energy (in eV) of that longest-wavelength photon? eV (c)What is its wavelength (in nm)? 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, ni,of the transition that generates the photon with the shortest wavelength? (Again, restrict your attention to the four illustrated transitions.) (e)What is that photon's energy (in eV)? ?eV (f)What is that photon's wavelength (in nm)? ? nm (g)Finally, consider all transitions from ni > 2 that end at nf = 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 series? ?nm

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter8: Atomic Structure

Section: Chapter Questions

Problem 96AP: The ion Be3+ makes an atomic transition from an n =: 3 state to an n = 2 state, (a) What is the...

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Question

The Balmer series for the hydrogen atom comprises electron energy transitions that end in the
nf = 2 state.

An illustration of energy levels shows the colors of the lines of the Balmer series. The bottom energy level in the diagram is n = 2, and an upward arrow indicates that energy increases with higher energy levels, labeled up to n = ∞, where E = 0.00 eV. The energy of n = 2 is −3.401 eV, n = 3 is −1.512 eV, n = 4 is −0.8504 eV, n = 5 is −0.5442 eV, and n = 6 is −0.378 eV. Balmer lines are produced when an electron jumps to n = 2 from any higher level. Red color is emitted during transition from n = 3, green color during transition from n = 4, blue color during transition from n = 5, and violet color during transition from n = 6.

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_i,of the transition that generates the photon with the longest wavelength? (Restrict your attention to the four illustrated transitions.)

n_i =

(b)What is the energy (in eV) of that longest-wavelength photon?

(c)What is its wavelength (in 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_i,of the transition that generates the photon with the shortest wavelength? (Again, restrict your attention to the four illustrated transitions.)

(e)What is that photon's energy (in eV)?

?eV

(f)What is that photon's wavelength (in nm)?

? nm

(g)Finally, consider all transitions from n_i > 2 that end at n_f = 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 series?

?nm

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E (eV)
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0.850 4
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the four illustrated transitions, each shown by a dow
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-3.401
hat is the initial quantum number, m, of the transition t
What is the energy (in eV) of that longest-wavelength phot
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#1

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