7.23. Light, Energy, and
the Hydrogen Atom

• a. Which
  has the greater wavelength, blue light or red light?
• b. How do
  the frequencies of blue light and red light compare?
• c. How
  does the energy of blue light compare with that of red light?
• d. Does blue
  light have a greater speed than red light?
• e. How
  does the energy of three photons from a blue light source compare with the
  energy of one photon of blue light from the same source? How does the
  energy of two photons corresponding to a wavelength of 451 nm (blue light)
  compare with the energy of three photons corresponding to a wavelength of
  704 nm (red light)?
• f. A
  hydrogen atom with an electron in its ground state interacts with a photon
  of light with a wavelength of 1.22 × 10^-6m. Could the electron
  make a transition from the ground state to a higher energy level? If it
  does make a transition, indicate which one. If no transition can occur,
  explain.
• g. If you
  have one mole of hydrogen atoms with their electrons in the n = 1 level,
  what is the minimum number of photons you would need to interact with
  these atoms in order to have all of their electrons promoted to the n = 3
  level? What wavelength of light would you need to perform this experiment?

7.24. Investigating
Energy Levels

Consider the hypothetical atom X that has one electron
like the H atom but has different energy levels. The energies of an electron in
an X atom are described by the equation

E = – (R_H/ n³)

where R_His the same as for hydrogen (2.179 ×10^-18J).
Answer the following questions,without calculating energy values.

• a. How
  would the ground-state energy levels of X and H compare?
• b. Would
  the energy of an electron in the n = 2 level of H be higher or lower than
  that of an electron in the n = 2 level of X? Explain your answer.
• c. How do
  the spacings of the energy levels of X and H compare?
• d. Which
  would involve the emission of a higher frequency of light, the transition
  of an electron in an H atom from the n = 5 to the n = 3 level or a similar
  transition in an X atom?
• e. Which
  atom, X or H, would require more energy to completely remove its electron?
• f. A
  photon corresponding to a particular frequency of blue light produces a
  transition from the n = 2 to the n = 5 level of a hydrogen atom. Could
  this photon produce the same transition (n = 2 to n = 5) in an atom of X?
  Explain.

Assignment
Chapter 8

Concept Explorations

8.29. Periodic Properties
I

A hypothetical element, X, has the following ionization
energy values:

First ionization energy: 900 kJ/mol

Second ionization energy: 1750 kJ/mol

Third ionization energy: 14,900 kJ/mol

Fourth ionization energy: 21,000 kJ/mol

Another element, Y, has the following ionization energy
values:

First ionization energy: 1200 kJ/mol

Second ionization energy: 2500 kJ/mol

Third ionization energy: 19,900 kJ/mol

Fourth ionization energy: 26,000 kJ/mol

• a. To what
  family of the periodic table would element X be most likely to belong?
  Explain?
• b. What
  charge would you expect element X to have when it forms an ion?
• c. If you
  were to place elements X and Y into the periodic table, would element Y be
  in the same period as element X? If not in the same period, where might
  they be relative to each other in the periodic table?
• d. Would
  an atom of Y be smaller or larger than an atom of X? Explain your
  reasoning.

8.30. Periodic Properties
II

Consider two hypothetical elements, W and Z. Element W
has an electron affinity of -150 kJ/mol, and element Z has an electron affinity
of -38 kJ/mol.

• a. If you
  have a W^–ion and a Z^–ion, from which ion
  would it require more energy to remove an electron? Explain your answer.
• b. If
  elements W and Z are in the same period of the periodic table, which atom
  would you expect to have the greater atomic radius? Why?
• c.
  Assuming that the elements are in the same period, which element would you
  expect to have the smaller first ionization energy?
• d. Do the
  valence electrons in element Z feel a greater effective nuclear charge
  than those in element W? Explain how you arrived at your answer.

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