Question

Without looking back in the text, write the electron configurations for the following: (a) Titanium \(Z=22\) (b) Phosphorus, \(Z=15\) (c) Argon, \(Z=18\) (d) Lanthanum, \(Z=57\)

Short answer

Titanium: \([Ar]3d^24s^2\); Phosphorus: \([Ne]3s^23p^3\); Argon: \([Ne]3s^23p^6\); Lanthanum: \([Xe]5d^16s^2\).

Step-by-step solution

Determine the Atomic Number

The atomic number (\(Z\)) of an element represents the number of electrons in a neutral atom of that element. For each of the elements, verify the atomic number matches provided (e.g., Titanium \(Z=22\), Phosphorus \(Z=15\), Argon \(Z=18\), Lanthanum \(Z=57\)).

Apply the Aufbau Principle

The Aufbau principle helps us determine the electron configuration by filling electron orbitals in increasing order of energy levels: \(1s\), \(2s\), \(2p\), \(3s\), \(3p\), \(4s\), \(3d\), \(4p\), \(5s\), \(4d\), \(5p\), \(6s\), \(4f\), \(5d\), \(6p\), and so on.

Determine the Electron Configuration for Titanium

Titanium (\(Z=22\)) has 22 electrons. Following the order from Step 2:1. \(1s^2\)2. \(2s^2\)3. \(2p^6\)4. \(3s^2\)5. \(3p^6\)6. \(4s^2\)7. \(3d^2\)Thus, the electron configuration for titanium is \([3d^2][4s^2][3p^6][3s^2][2p^6][2s^2][1s^2]\) or \([Ar]3d^24s^2\).

Determine the Electron Configuration for Phosphorus

Phosphorus (\(Z=15\)) has 15 electrons. Following the order from Step 2:1. \(1s^2\)2. \(2s^2\)3. \(2p^6\)4. \(3s^2\)5. \(3p^3\)Thus, the electron configuration for phosphorus is \([3p^3][3s^2][2p^6][2s^2][1s^2]\) or \([Ne]3s^23p^3\).

Determine the Electron Configuration for Argon

Argon (\(Z=18\)) has 18 electrons. Following the order from Step 2:1. \(1s^2\)2. \(2s^2\)3. \(2p^6\)4. \(3s^2\)5. \(3p^6\)Thus, the electron configuration for argon is \([3p^6][3s^2][2p^6][2s^2][1s^2]\) or \([Ne]3s^23p^6\).

Determine the Electron Configuration for Lanthanum

Lanthanum (\(Z=57\)) has 57 electrons. Following the order from Step 2:1. \(1s^2\)2. \(2s^2\)3. \(2p^6\)4. \(3s^2\)5. \(3p^6\)6. \(4s^2\)7. \(3d^10\)8. \(4p^6\)9. \(5s^2\)10. \(4d^10\)11. \(5p^6\)12. \(6s^2\)13. \(5d^1\)Thus, the electron configuration for lanthanum is \([5d^1][6s^2][4f^0][5p^6][4d^{10}][5s^2][4p^6][3d^{10}][4s^2][3p^6][3s^2][2p^6][2s^2][1s^2]\) or \([Xe]5d^16s^2\).

Key concepts

Atomic Number

The atomic number of an element is a fundamental concept in chemistry. It is represented by the symbol \(Z\) and corresponds to the number of protons in the nucleus of an atom. For a neutral atom, the atomic number also equals the number of electrons. Thus, it plays a critical role in determining an element’s electron configuration. Here’s why knowing the atomic number is crucial:

• Identifies the Element: Each element has a unique atomic number. For instance, hydrogen has \(Z=1\), and carbon has \(Z=6\), distinguishing them on the periodic table.
• Determines Electron Arrangement: The atomic number directly indicates how many electrons need to be placed around the nucleus, which influences the chemical properties of the element.

When solving electron configurations, begin by verifying the atomic number to ascertain the correct number of electrons to organize within the orbitals.

Aufbau Principle

The Aufbau principle is a guideline used to determine the electron configuration of an atom in its ground state. It states that electrons are added to the lowest energy orbitals first before occupying higher energy levels. This method is like "building up" the electron configuration, starting from the least energy-demanding state. Here's how it typically works:

• Sequential Filling: Electrons fill the orbitals starting with the lowest available (e.g., \(1s\)), proceeding to \(2s\), \(2p\), and so forth.
• Order of Energy Levels: The order follows a known sequence informed by the energy of the orbitals: \(1s\), \(2s\), \(2p\), \(3s\), \(3p\), \(4s\), \(3d\), \(4p\), etc.

By adhering to the Aufbau principle, one can write out the electron configurations correctly, ensuring that the more stable configurations are calculated first.

Lanthanide Series

The lanthanide series refers to a set of 15 metallic elements with atomic numbers ranging from 57 to 71, positioned from Lanthanum (\(Z=57\)) to Lutetium (\(Z=71\)). These elements are often called rare earth elements, although they are not particularly rare in terms of abundance. Here's what makes them unique:

• Electron Filling: The lanthanides see the filling of 4f orbitals. Starting with Cerium (\(Z=58\)), the 4f subshell is gradually filled across the series.
• Chemical Similarity: Lanthanides have very similar properties due to the often similar electron configurations, particularly due to partly filled 4f orbitals.

Writing electron configurations for lanthanides can involve lengthy notations due to many electrons, but shorthand using the preceding noble gas (e.g., \([Xe]\)) helps simplify this process.

Orbital Filling Order

Understanding the orbital filling order is key in writing electron configurations accurately. This involves knowing the sequence in which atomic orbitals are filled as electrons are added to an atom. The order isn’t strictly sequential on the periodic table but follows the energy levels of the orbitals:

• Sequence of Orbitals: The canonical sequence is \(1s\), \(2s\), \(2p\), \(3s\), \(3p\), \(4s\), \(3d\), \(4p\), \(5s\), and so forth.
• Energy-Based Order: Remember, orbitals are filled based on increasing energy values, so sometimes the \(4s\) is filled before the \(3d\) despite the latter belonging to the previous shell numerically.

This order can be remembered using the n + l rule, where n is the principal quantum number, and l is the azimuthal quantum number. However, mnemonic devices or periodic table guidance can also be quite helpful.