Question

Consider these elements: \(\mathrm{N}, \mathrm{Mg}, \mathrm{O}, \mathrm{F}, \mathrm{Al}\) $$ \begin{array}{l}{\text { a. Write the electron configuration for each element. }} \\ {\text { b. Arrange the elements in order of decreasing atomic radius. }} \\ {\text { c. Arrange the elements in order of fincreasing ionization energy. }} \\ {\text { d. Use the electron configurations in part a to explain the differences }} \\ {\text { between your answers to parts b and c. }}\end{array} $$

Short answer

Electron configurations are N:1s²2s²2p³, Mg:1s²2s²2p⁶3s², O:1s²2s²2p⁴, F:1s²2s²2p⁵, Al:1s²2s²2p⁶3s²3p¹. Atomic radius decreases: Mg > Al > N > O > F. Ionization energy increases: Mg < Al < N < O < F. Differences are due to changes in nuclear charge and electron shell level across periods and down groups.

Step-by-step solution

Writing Electron Configurations

To write the electron configurations for each element, identify the number of electrons and fill in the orbitals according to Hund's rule and the Pauli exclusion principle. For the given elements, the electron configurations are as follows: Nitrogen (N, atomic number 7): 1s²2s²2p³, Magnesium (Mg, atomic number 12): 1s²2s²2p⁶3s², Oxygen (O, atomic number 8): 1s²2s²2p⁴, Fluorine (F, atomic number 9): 1s²2s²2p⁵, Aluminum (Al, atomic number 13): 1s²2s²2p⁶3s²3p¹.

Ordering by Decreasing Atomic Radius

Atomic radius decreases across a period due to increasing nuclear charge pulling electrons closer to the nucleus. For the given elements within the same period (N, O, F), the atomic radius decreases as we move from left to right. Mg and Al are from the third period and have a higher atomic radius than second-period elements. However, Mg has a slightly larger atomic radius than Al. Therefore, the order from largest to smallest atomic radius is: Mg > Al > N > O > F.

Ordering by Increasing Ionization Energy

Ionization energy increases across a period and decreases down a group. For the given elements within the same period (N, O, F), ionization energy increases from N to F. Between the periods, second-period elements have higher ionization energies than those in the third period due to a greater effective nuclear charge. Hence, the order of increasing ionization energy is: Mg < Al < N < O < F.

Explaining Differences in Atomic Radius and Ionization Energy

The differences in atomic radius and ionization energy can be accounted for by considering effective nuclear charge and electron shell level. As we move across a period, the increasing nuclear charge and the identical shielding effect lead to a smaller atomic radius and higher ionization energy. As we move down a group, the addition of energy levels results in a larger atomic radius and a lower ionization energy.

Key concepts

Atomic Radius

Understanding the atomic radius is crucial in grasping the structure of the periodic table. This term refers to the size of an atom, specifically half the distance between the nuclei of identical neighboring atoms. Imagine a balloon where the nucleus is at the center and the electron cloud is the surface; the atomic radius is half the diameter of that balloon.

To understand why atomic radius decreases across a period, consider that each subsequent element adds a proton to its nucleus and an electron to the same energy level. More protons mean a stronger attraction to the electrons, pulling them closer to the nucleus and shrinking the atomic balloon. This is why, when arranging elements like Nitrogen, Oxygen, and Fluorine, the radius gets smaller with each consecutive element.

Periodic Trends in Atomic Radius

As you move from left to right across a period, the atomic radius decreases. This is because the effective nuclear charge increases, attracting electrons more strongly and decreasing the size of the atom. But as you go down a group, the radius increases because you're adding more electron shells, like layers to an onion, making the atom larger even though the nucleus is pulling on the outer electrons more strongly.

Ionization Energy

Ionization energy is the energy needed to remove the outermost electron from an atom in its gaseous state. It can be thought of like climbing a hill - the higher the ionization energy, the bigger the metaphorical hill, and the harder it is to remove an electron.

Ionization energy generally increases across a period because as the atomic radius decreases, electrons are closer to the attractive pull of the nucleus, making it harder to take one away. This is why Fluorine has a higher ionization energy than Oxygen or Nitrogen. However, ionization energy decreases down a group because outer electrons are further from the nucleus and not held as tightly.

Explaining Ionization Energy Trends

When elements like Magnesium and Aluminum are considered, their ionization energies are lower than the elements in the second period because their outermost electrons are further away from the nucleus, requiring less energy to remove that electron.

Hund's Rule

Hund's rule addresses the distribution of electrons among equally energetically favorable orbitals. Imagine you have a row of seats on a bus with one person in each seat — this is like Hund's rule for electrons. Each electron, or passenger, picks its own orbital seat before doubling up.

By spreading out before pairing up, electrons minimize repulsion between themselves due to their like charges. This rule explains why Nitrogen, with an atomic number of 7, fills its p orbitals with three unpaired electrons: one electron in each orbital before any pairing occurs.

Applying Hund's Rule

When you see the electron configuration for Oxygen, after following Hund's rule, you'll notice that one of the p orbitals will have a pair of electrons because there are more than three electrons to distribute in three p orbitals.

Pauli Exclusion Principle

The Pauli exclusion principle is a quantum law stating that no two electrons in an atom can have the same set of four quantum numbers. Essentially, it's a rule that forbids electron roommates from being completely identical. Each electron in an orbital must have an opposite spin to its partner, like dance partners facing opposite directions.

This principle is what ensures electrons within the same orbital have opposite spins and is the reason why we see the electron arrangements of atoms like those in Fluorine and Oxygen having paired and unpaired configurations.

Impact on Electron Configurations

In Nitrogen's configuration, each electron in the 2p orbitals has a unique set of quantum numbers, fulfilling the Pauli exclusion principle as they're unpaired with unique spins. However, when an electron is added (as in Oxygen and Fluorine), some electrons must pair up, but they still maintain opposite spins to comply with the principle.

Effective Nuclear Charge

Effective nuclear charge (ENC) is the net positive charge experienced by an electron in a multi-electron atom. It's not just the charge of the nucleus but the charge felt by an electron when you take into account both the attraction to the nucleus and the repulsion from other electrons.

As we add electrons across a period, even though they are added to the same energy level, the ENC increases because additional protons are also added to the nucleus, which has more pulling power over the same number of inner electrons.

Calculating ENC

Aluminum has an ENC less than Fluorine's because its outer electrons are further from the nucleus and more shielded by the inner electrons. The greater ENC for elements in the same period increases the ionization energy and decreases the atomic radius. This concept is fundamentally why elements across a period become smaller and require more energy to remove an electron.