Question

Suppose that means were available for stripping 29 electrons from \({ }_{30} \mathrm{Zn}\) in vapours of this metal. The ionization energy for the last electron is (a) \(11.5 \mathrm{keV}\) (b) \(12.24 \mathrm{keV}\) (c) \(13.6 \mathrm{eV}\) (d) \(408 \mathrm{eV}\)

Short answer

The ionization energy for the last electron is (b) \(12.24 keV\).

Step-by-step solution

- Understanding the concept of ionization energy

Ionization energy is the energy required to remove an electron from a gaseous atom or ion. The greater the charge on the ion, the more energy is needed to remove an electron because the electron is being removed from an increasingly positive ion, and thus more strongly attracted to the nucleus. In this case, we are looking for the ionization energy of the last electron from \text{\({ }_{30}\text{Zn}^{29+}\)}, which is highly charged.

- Considering given options

Ionization energies are typically in the realm of electronvolts (eV) for outer electrons. However, since we are dealing with a very highly charged ion, we should expect the ionization energy for the last electron to be significantly higher than typical values because the electron is being removed from a nucleus with a very high positive charge.

- Eliminating unlikely options

Options (a), (c), and (d) can be compared to recognize that (c) 13.6 eV is the ionization energy for a neutral hydrogen atom. Therefore this value is too low for a highly charged zinc ion. Option (d) 408 eV is also relatively low. Considering that each successive ionization energy is larger than the previous (due to an increasing positive charge), we can eliminate options (c) and (d).

- Identifying the correct ionization energy

By eliminating the lower values, we narrow it down to options (a) and (b). Since we're dealing with the removal of the 29th electron and the nucleus has a significantly higher positive charge, the ionization energy is expected to be in the keV range. Thus, the only plausible options are (a) and (b).

- Choosing the most accurate value

Between the remaining options (a) and (b), the value for (b) \text{\(12.24 keV\)} is slightly higher than (a) \text{\(11.5 keV\)}, which is more consistent with the high ionization energy expected for the removal of the last electron from such a highly charged ion.

Key concepts

Physical Chemistry

Physical chemistry is a branch of chemistry that deals with the study of how matter behaves on a molecular and atomic level, and how chemical reactions occur. It provides an in-depth look at the physical structures of materials and the energy transformations that accompany chemical changes. In the context of ionization energy, physical chemistry seeks to understand the energy changes that occur when an electron is removed from an atom or molecule. This concept is pivotal for comprehending reactions and properties related to the atomic scale, such as reactivity, bonding, and the periodic trends of elements.

Key topics in physical chemistry, such as thermodynamics, kinetics, and quantum chemistry, all play a role in the understanding of ionization energy. These areas help to predict the behavior of atoms during the electron removal process, and they underline how energy is absorbed or released during such transformations. For students, mastering the principles of physical chemistry is crucial for explaining phenomena observed both in nature and in experimental settings.

Electron Removal

Electron removal, more commonly known as ionization, is the process of ejecting an electron from an atom or ion. The difficulty of removing an electron, and therefore the amount of energy required, increases as we remove more and more electrons because the positive charge of the nucleus holds the remaining electrons more strongly. Ionization energy is a quantifiable physical quantity expressing the energy required in this process.

In a classroom setting, electron removal can be demonstrated through experiments or simulated using computer software. Understanding this process is important for students as it ties into various aspects of atomic behavior, including the formation of ions, the reactivity of elements, and the principles governing intermolecular forces.

Chemical Elements

Chemical elements are pure substances consisting of one type of atom, distinguished by their atomic number, which is the number of protons in the nucleus. Each element possesses unique properties, including a characteristic ionization energy. The concept of ionization energy is employed to understand the reactivity of an element, the nature of its bonds, and its position in the Periodic Table.

For example, elements with low ionization energies tend to form cations easily and are typically metals. In contrast, nonmetals usually have higher ionization energies and are more likely to gain electrons to become anions. This is fundamental knowledge in understanding the theory behind the reactivity and classification of elements, which is a central theme in chemistry education.

Atomic Structure

Atomic structure refers to the arrangement of subatomic particles in an atom, including protons, neutrons in the nucleus, and electrons in various energy levels. The distribution of electrons across the different orbitals and shells significantly influences an atom’s chemical properties, including its ionization energy. A deeper understanding of atomic structure is fundamental when discussing ionization energy, as it relates directly to the energy required to remove an electron from an energy level.

From the perspective of teaching and learning, students should grasp the concept of electron shells and the nuclear charge to understand why inner electrons are more difficult to remove than those in outer shells. This also relates to the periodic trends observed across the Periodic Table, such as the increase of ionization energy from left to right across a period and the decrease down a group. These trends can be explained by the atomic structure and the effect of nuclear charge on electron affinity.