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.

Verified step by step guidance

1. Step 1: First, we need to calculate the energy of the ultraviolet light used in the PES experiment. The energy of a photon can be calculated using the equation E = hc/λ, where h is Planck's constant (6.626 x 10^-34 J.s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of the light in meters. Convert the wavelength from nm to m by multiplying by 1 x 10^-9.
2. Step 2: The energy calculated in step 1 is the energy of the photons used in the PES experiment. This energy is used to remove electrons from the mercury atoms, so it corresponds to the ionization energy of mercury.
3. Step 3: Now, we need to compare this ionization energy with the first ionization energies of the halogen elements. The first ionization energies of the halogens can be found in Figure 7.10 or in a table of ionization energies.
4. Step 4: Compare the ionization energy of mercury calculated in step 2 with the first ionization energies of the halogens. Look for the halogen whose first ionization energy is closest to that of mercury.
5. Step 5: The halogen with the first ionization energy closest to that of mercury is the answer to the problem. Remember that ionization energy is the energy required to remove an electron from an atom, so a similar ionization energy means that it requires a similar amount of energy to remove an electron from the mercury atom and the halogen atom.

Key Concepts

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 is foundational for techniques like photoelectron spectroscopy (PES), as it demonstrates the interaction between light and matter, allowing for the measurement of the energy required to remove electrons from atoms.

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 critical property of elements that influences their chemical behavior and reactivity. In the context of PES, ionization energy can be determined by analyzing the kinetic energy of emitted electrons when a sample is irradiated with light.

Ultraviolet Photoelectron Spectroscopy (PES)

Ultraviolet photoelectron spectroscopy (PES) is an analytical technique used to study the electronic structure of atoms and molecules. By directing monochromatic ultraviolet light onto a sample, PES measures the kinetic energy of emitted electrons, allowing researchers to calculate ionization energies and gain insights into the energy levels of electrons in different elements.