Question

Use electron configurations to explain why the ionization energy for calcium is greater than that for potassium.

Short answer

The ionization energy for calcium is greater than that for potassium because Calcium’s last energy level 4s is fully filled with two electrons providing additional stability, while potassium’s energy level 4s is only half-filled with one electron. It's more difficult to remove an electron from a fully filled energy level, thus calcium has a greater ionization energy.

Step-by-step solution

Understand Ionization Energy

The first thing to understand is what ionization energy is. Ionization energy is the amount of energy required to remove an electron from an atom or a positive ion. The energy required to remove the first electron is referred to as the first ionization energy, while the energy required to remove the second electron is referred to as the second ionization energy, and so on.

Examine Electron Configurations of Potassium and Calcium

Next, examine the electron configurations of potassium and calcium. Potassium (K) has the electron configuration \([Ar] 4s1\), while calcium (Ca) has the electron configuration \([Ar] 4s2\). This means that potassium has one electron in its 4s energy level, while calcium has two electrons in its 4s energy level.

Apply Electron Configuration to Ionization Energy

In the energy levels of an atom, the s-orbital can hold a maximum of two electrons. The 4s level of calcium is fully occupied with two electrons, while in potassium the 4s level is half-occupied, with only one electron. According to Hund’s rule, half-filled and fully filled energy levels have extra stability. Therefore, it is harder to remove an electron from the fully filled 4s energy level of calcium than the half filled 4s energy level of potassium, thus ionization energy of calcium is higher than the ionization energy of potassium.

Key concepts

Electron Configuration

Understanding electron configuration is essential when it comes to explaining various properties of elements, including ionization energy. Essentially, electron configuration is the distribution of electrons of an atom or molecule in atomic and molecular orbitals.

For instance, take potassium (K) which has the configuration \([Ar] 4s^1\), indicating that beyond the noble gas argon core, there is one electron in the 4s subshell. On the other hand, calcium (Ca) follows with \([Ar] 4s^2\), signifying two electrons occupying the 4s subshell. This represents how far an electron is from the nucleus and how tightly it’s being held by the atom's charge.

Understanding the intricacies of electron configuration allows students to see why certain electrons are removed more easily from atoms during the ionization process, giving a hint at the atom’s reactivity and chemical properties.

First Ionization Energy

First ionization energy is a term that can trip up many students, but it’s a simple concept at its core. It's the amount of energy needed to remove the most loosely held electron, the outermost electron, of an isolated gaseous atom to form a cation.

For example, you might wonder why it's harder to remove the first electron from calcium than it is from potassium. This comes down to both the energy level the electron occupies and the effective nuclear charge - the net positive charge experienced by the electron. Calcium's outer electrons are shielded by a similar electron configuration to potassium but have a stronger attraction to the nucleus due to the additional protons in calcium. Therefore, more energy is required to remove one of the electrons from calcium's outer orbital, which is reflected in its higher first ionization energy.

Hund's Rule

Hund's rule seems like an obscure principle, but it's crucial for explaining why certain electron configurations are more stable. The rule states that electrons will occupy empty orbitals before they pair up.

That's because electrons are negatively charged and, like magnets, similar charges repel each other. Placing one electron in each available orbital minimizes repulsion between them. Once every orbital in a sublevel is singly occupied, electrons can start to pair up.

For elements like calcium and potassium, this principle helps explain the stability of their electron configurations. Calcium’s 4s sublevel is fully occupied with two electrons, which makes it more stable (and thus, harder to ionize) than potassium's half-filled 4s sublevel, which only contains one electron and has a lower ionization energy.

Atomic Structure

To truly grasp concepts like ionization energy, an understanding of atomic structure is imperative. An atom is comprised of a nucleus that contains protons and neutrons, around which electrons orbit in various shells and subshells.

The organization of these electrons is governed by the rules of quantum mechanics, with electrons filling lower energy levels before higher ones - a concept often referred to as the 'Aufbau principle'. Atomic structure dictates an atom's chemical behavior, and it's the interplay between the positively charged nucleus and the negatively charged electrons that dictates how easily an atom will give up those electrons – in other words, its ionization energy.

With potassium and calcium, for instance, the difference in their atomic number (which determines the number of protons in the nucleus) also influences their ionization energies. More protons mean a stronger pull on the electrons, contributing to a higher ionization energy as seen in calcium compared to potassium.