1. Excitations in the Bohr model. One can excite the electronic state of an atom by hitting it with a photon whose energy corresponds exactly to the energy spacing between two energy states. This is the essence of spectroscopy. (a) According to the Bohr model for a hydrogen atom, what is the energy difference between the ground state (n = 1) and each of the first (n = 2), second (n = 3), and third (n = 4) excited states? (Note: the electron always starts in the ground state). What wavelength of light, in nanometers, is needed to cause each of these excitations? (b) What region of the electromagnetic spectrum do the wavelengths from part (a) corre- spond to? (c) What wavelength of light (in nm) is required to ionize the atom? What happens if you hit the atom with an even shorter wavelength of light? (d) The Bohr model can also be used to describe other one-electron atoms such as He*, Li?+, etc. How does the energy for these excitations change qualitatively as the nuclear charge increases?

Principles of Modern Chemistry
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Chapter4: Introduction To Quantum Mechanics
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4. Excitations in the Bohr model. One can excite the electronic state of an atom by hitting
it with a photon whose energy corresponds exactly to the energy spacing between two energy
states. This is the essence of spectroscopy.
(a) According to the Bohr model for a hydrogen atom, what is the energy difference between
the ground state (n = 1) and each of the first (n = 2), second (n = 3), and third (n = 4)
excited states? (Note: the electron always starts in the ground state). What wavelength
of light, in nanometers, is needed to cause each of these excitations?
(b) What region of the electromagnetic spectrum do the wavelengths from part (a) corre-
spond to?
(c) What wavelength of light (in nm) is required to ionize the atom? What happens if you
hit the atom with an even shorter wavelength of light?
(d) The Bohr model can also be used to describe other one-electron atoms such as He+,
Li2+, etc. How does the energy for these excitations change qualitatively as the nuclear
charge increases?
Transcribed Image Text:4. Excitations in the Bohr model. One can excite the electronic state of an atom by hitting it with a photon whose energy corresponds exactly to the energy spacing between two energy states. This is the essence of spectroscopy. (a) According to the Bohr model for a hydrogen atom, what is the energy difference between the ground state (n = 1) and each of the first (n = 2), second (n = 3), and third (n = 4) excited states? (Note: the electron always starts in the ground state). What wavelength of light, in nanometers, is needed to cause each of these excitations? (b) What region of the electromagnetic spectrum do the wavelengths from part (a) corre- spond to? (c) What wavelength of light (in nm) is required to ionize the atom? What happens if you hit the atom with an even shorter wavelength of light? (d) The Bohr model can also be used to describe other one-electron atoms such as He+, Li2+, etc. How does the energy for these excitations change qualitatively as the nuclear charge increases?
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