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Atoms, Energy, and the Periodic Table

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Assignment Chapter 7
Concept Explorations
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 = - (RH / n3)
where RHis 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.

Solution Summary

A number of problems based on atomic structure are solved.

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Assignment Chapter 7
Concept Explorations
7.23. Light, Energy, and the Hydrogen Atom

• a. Which has the greater wavelength, blue light or red light?
Red

• b. How do the frequencies of blue light and red light compare?
As frequency is inversely proportional to wavelength, blue light should have greater frequency.

• c. How does the energy of blue light compare with that of red light?
Energy is directly proportional to frequency, hence blue light should have greater energy.

• d. Does blue light have a greater speed than red light?
Speed does not depend on the frequency or wavelength, hence both will have same speed.

• 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)?
Energy of 3 photons will not be that different, basically 3 times that of a single photon. For blue light of 451 nm,
E = (6.625 x 10-34 Js x 3 x 108 m) / (451 x 10-9 m) = 4.41 x 10-19 J
Hence for 2 photons, E = 8.82 x 10-19 J
Similarly, for red light, E = 2.82 x 10-19 J
For 3 photons E = 8.47 x 10-19 J

• 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.
The photon like above will have E = 1.63 x x 10-19 J
The electron for H has E = 2.18 x x 10-18 J
Hence there is not enough energy to remove the electron as photon has less energy than the electron in the ground state of H.

• 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 ...

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