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Ch.7 - Periodic Properties of the Elements
All textbooksBrown 14th EditionCh.7 - Periodic Properties of the ElementsProblem 111b
Chapter 7, Problem 111b

One way to measure ionization energies is ultraviolet photoelectron spectroscopy (PES), a technique based on the photoelectric effect. (Section 6.2) In PES, monochromatic light is directed onto a sample, causing electrons to be emitted. The kinetic energy of the emitted electrons is measured. The difference between the energy of the photons and the kinetic energy of the electrons corresponds to the energy needed to remove the electrons (that is, the ionization energy). Suppose that a PES experiment is performed in which mercury vapor is irradiated with ultraviolet light of wavelength 58.4 nm. (b) Write an equation that shows the process corresponding to the first ionization energy of Hg.

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1
Understand the concept of ionization energy: Ionization energy is the energy required to remove an electron from an atom or ion in its gaseous state.
Identify the process for the first ionization energy: The first ionization energy involves removing the outermost electron from a neutral atom.
Write the general equation for the ionization process: For a generic element X, the equation is X(g) → X⁺(g) + e⁻.
Apply the equation to mercury (Hg): Replace X with Hg to represent the ionization of mercury.
The equation for the first ionization energy of mercury is: Hg(g) → Hg⁺(g) + e⁻.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ionization Energy

Ionization energy is the amount of energy required to remove an electron from an atom or ion in its gaseous state. It is a crucial concept in understanding the reactivity and stability of elements, as it influences how easily an atom can lose electrons to form positive ions. The first ionization energy specifically refers to the energy needed to remove the outermost electron from a neutral atom.
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Photoelectric Effect

The photoelectric effect is a phenomenon where electrons are emitted from a material when it is exposed to light of sufficient energy. This effect demonstrates the particle nature of light, as photons must have enough energy to overcome the binding energy of electrons in the material. In the context of photoelectron spectroscopy, this principle is used to measure the kinetic energy of emitted electrons, which helps determine ionization energies.
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Ultraviolet Photoelectron Spectroscopy (PES)

Ultraviolet photoelectron spectroscopy (PES) is an analytical technique used to study the electronic structure of atoms and molecules. In PES, a sample is irradiated with ultraviolet light, causing the emission of electrons. By measuring the kinetic energy of these electrons and knowing the energy of the incident photons, one can calculate the ionization energy of the sample, providing insights into its electronic configuration and chemical properties.
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Related Practice
Textbook Question

Moseley established the concept of atomic number by studying X rays emitted by the elements. The X rays emitted by some of the elements have the following wavelengths: Element Wavelength (pm) Ne 1461 Ca 335.8 Zn 143.5 Zr 78.6 Sn 49.1 (b) Plot the square root of n versus the atomic number of the element. What do you observe about the plot? (e) A particular element emits X rays with a wavelength of 98.0 pm. What element do you think it is?

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Textbook Question

Moseley established the concept of atomic number by studying X rays emitted by the elements. The X rays emitted by some of the elements have the following wavelengths: Element Wavelength (pm) Ne 1461 Ca 335.8 Zn 143.5 Zr 78.6 Sn 49.1 (d) Use the result from part (b) to predict the X-ray wavelength emitted by iron.

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Textbook Question

Moseley established the concept of atomic number by studying X rays emitted by the elements. The X rays emitted by some of the elements have the following wavelengths: Element Wavelength (pm) Ne 1461 Ca 335.8 Zn 143.5 Zr 78.6 Sn 49.1 (e) A particular element emits X rays with a wavelength of 98.0 pm. What element do you think it is?

Textbook Question

One way to measure ionization energies is ultraviolet photoelectron spectroscopy (PES), a technique based on the photoelectric effect. (Section 6.2) In PES, monochromatic light is directed onto a sample, causing electrons to be emitted. The kinetic energy of the emitted electrons is measured. The difference between the energy of the photons and the kinetic energy of the electrons corresponds to the energy needed to remove the electrons (that is, the ionization energy). Suppose that a PES experiment is performed in which mercury vapor is irradiated with ultraviolet light of wavelength 58.4 nm. (c) The kinetic energy of the emitted electrons is measured to be 1.72 × 10-18 J. What is the first ionization energy of Hg, in kJ/mol?

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Textbook Question

One way to measure ionization energies is ultraviolet photoelectron spectroscopy (PES), a technique based on the photoelectric effect. (Section 6.2) In PES, monochromatic light is directed onto a sample, causing electrons to be emitted. The kinetic energy of the emitted electrons is measured. The difference between the energy of the photons and the kinetic energy of the electrons corresponds to the energy needed to remove the electrons (that is, the ionization energy). Suppose that a PES experiment is performed in which mercury vapor is irradiated with ultraviolet light of wavelength 58.4 nm. (d) Using Figure 7.10, determine which of the halogen elements has a first ionization energy closest to that of mercury.

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Textbook Question
Mercury in the environment can exist in oxidation states 0, +1, and +2. One major question in environmental chemistry research is how to best measure the oxidation state of mercury in natural systems; this is made more complicated by the fact that mercury can be reduced or oxidized on surfaces differently than it would be if it were free in solution. XPS, X-ray photoelectron spectroscopy, is a technique related to PES (see Exercise 7.111), but instead of using ultraviolet light to eject valence electrons, X rays are used to eject core electrons. The energies of the core electrons are different for different oxidation states of the element. In one set of experiments, researchers examined mercury contamination of minerals in water. They measured the XPS signals that corresponded to electrons ejected from mercury's 4f orbitals at 105 eV, from an X-ray source that provided 1253.6 eV of energy 11 ev = 1.602 * 10-19J2. The oxygen on the mineral surface gave emitted electron energies at 531 eV, corresponding to the 1s orbital of oxygen. Overall the researchers concluded that oxidation states were +2 for Hg and -2 for O. (b) Compare the energies of the 4f electrons in mercury and the 1s electrons in oxygen from these data to the first ionization energies of mercury and oxygen from the data in this chapter.
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