Question

Describe how the ionization energies of the ions \(\mathrm{Be}^{+}, \mathrm{B}^{+}, \mathrm{C}^{+}, \mathrm{N}^{+}, \mathrm{O}^{+}, \mathrm{F}^{+}, \mathrm{Ne}^{+},\) and \(\mathrm{Na}^{+}\) vary with atomic number.

Short answer

As atomic number increases, ionization energy generally increases due to the increased nuclear charge. However, ions with half-filled or fully filled sub-shells have higher ionization energies due to increased stability.

Step-by-step solution

Analyze the electron configuration

First, let's start by writing down the electron configuration for each ion. Note that each ion is a positively charged ion, meaning that it has lost one electron compared to the neutral atom. For the first ion, \(\mathrm{Be}^{+}\), the electron configuration of the neutral atom \(Be\) is \(1s^22s^2\). So, for \(\mathrm{Be}^{+}\), which has lost an electron, the configuration would be \(1s^22s^1\). Similarly, figure out the electron configuration for each of the other ions.

Analyze the trend in ionization energies based on electron configuration

Next, let's analyze how the electron configuration affects the ionization energy. Atoms that have half-filled or fully filled sub-shells have more stability, hence they have higher ionization energies. This is because these stable configurations are more tightly held by the nucleus, and more energy is needed to remove an electron. Also, as atomic number (which relates to nuclear charge) increases, the attractive force on the electrons increases. This means the ionization energy generally increases with an increase in atomic number.

Predict the variation in ionization energies

Comparing the electron configurations and knowing the factors that affect ionization energy, we predict that as atomic number increases, ionization energy will generally increase - provided that the increase in atomic number does not result in an ion with a more stable half-filled or fully filled sub-shell configuration. In those cases, the ion with the more stable configuration will have a higher ionization energy.

Key concepts

Electron Configuration

The electron configuration of an atom or ion describes the distribution of its electrons among different energy levels, sublevels, or orbitals. Each orbital can hold a specific number of electrons, described by subshells such as s, p, d, and f.
- Each subshell has a capacity: s can hold 2, p can hold 6, and so on.
- An electron configuration like \(1s^2 2s^1\) means there are two electrons in the 1s subshell and one electron in the 2s subshell.
For ions, the electron configuration changes as electrons are added or removed. In positively charged ions (cations), like the ones in this exercise, an electron is lost. For instance, a neutral Beryllium (\text{Be}) atom has the configuration \\(1s^2 2s^2\), but \\(\text{Be}^+\) loses one electron, resulting in \\(1s^2 2s^1\). This change influences the ion's properties, such as ionization energy.

Atomic Number

The atomic number, denoted as Z, reflects the number of protons in an atom's nucleus. This unique number determines the element's identity and position in the periodic table.
- The atomic number also equals the number of electrons in a neutral atom, impacting electron configuration.
- As the atomic number increases across a period, elements exhibit a greater nuclear charge, influencing their chemical behavior.
In the scenario of ions \from \(\text{Be}^+\) to \(\text{Na}^+\), the atomic number increases, illustrating a trend in physical properties such as ionization energies.
Higher atomic numbers usually result in greater ionization energies because of stronger effective nuclear charges, which more tightly hold electrons. Understanding atomic numbers provides insights into atomic interactions and trends.

Nuclear Charge

Nuclear charge refers to the total charge of the nucleus, equating to the number of protons present. As the core positive charge, it attracts electrons, affecting their energy levels and behavior.
- Effective nuclear charge (\(Z_{\text{eff}}\)) considers electron shielding, reflecting the net attraction an electron feels.
- Higher nuclear charges lead to tighter attraction to electrons, affecting ionization energy.
As we move across a period in the periodic table, the nuclear charge increases. This phenomenon aligns with an increase in the atomic number. For ions, particularly those like \\(\text{N}^+\) or \\(\text{O}^+\), this increased nuclear charge means removing an electron requires more energy, thus explaining their higher ionization energies compared to ions with lower nuclear charges.

Sub-shell Stability

Sub-shell stability refers to the arrangement of electrons in an atom that provides inherent balance and minimizes energy. This concept is about achieving half-filled or fully filled subshells, which are especially stable configurations. This stability plays into ionization energy calculations.
- Half-filled subshells, like \\(\text{N}^+\), have stability due to electron symmetry.
- Fully filled subshells, like the one seen with \\(\text{Ne}^+\), are even more stable.
Stable electron configurations require higher energy to remove an electron, increasing ionization energy. Understanding sub-shell stability helps predict ionization trends across the periodic table and explains anomalies, like why certain elements might not follow a straightforward increase in ionization energy as the atomic number increases. Recognizing stable states helps in explaining patterns in ionization energies among the elements and their ions.