Problem 4 - Chemistry and Chemical Reactivity

Question

Using spdf notation, give the electron configuration of vanadium, \(V\), an element found in some brown and red algae and some toadstools.

Step-by-Step Solution

Answer

Vanadium's electron configuration is \([1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^3]\).

Step 1: Determine the Atomic Number

The first step is to find the atomic number of vanadium (\(V\)). Vanadium is element number 23 on the periodic table. This means that a neutral vanadium atom has 23 electrons.

Step 2: Understanding Electron Configuration Notation

Electron configuration is written using spdf notation where each letter (s, p, d, and f) corresponds to a type of orbital, and the superscript indicates the number of electrons in those orbitals. For example, \(1s^2\) means that there are 2 electrons in the 1s orbital.

Step 3: Filling the Orbitals Sequentially

Electrons fill orbitals in a specific sequence based on energy levels. The sequence is:1. \(1s\)2. \(2s\)3. \(2p\)4. \(3s\)5. \(3p\)6. \(4s\)7. \(3d\)Following this sequence, we fill up electrons up to 23 for vanadium.

Step 4: Writing the Electron Configuration

Using the filling order, we write the electron configuration for vanadium:- \(1s^2\) : 2 electrons- \(2s^2\) : 2 electrons- \(2p^6\) : 6 electrons- \(3s^2\) : 2 electrons- \(3p^6\) : 6 electrons- \(4s^2\) : 2 electrons- \(3d^3\) : 3 electronsThe total is 2+2+6+2+6+2+3 = 23 electrons.

Step 5: Final Check

Verify that the electron count matches vanadium's atomic number, which is 23, ensuring the configuration is \([1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^3]\).

Key Concepts

Atomic Number

The atomic number is a fundamental property of an element that tells us the number of protons in the nucleus of its atoms. It also represents the number of electrons in a neutral atom. For example, vanadium ( V ) has an atomic number of 23, which means:

• It has 23 protons in its nucleus.
• It also contains 23 electrons orbiting around the nucleus in a neutral state.

Understanding the atomic number is crucial as it is the starting point for determining the electron configuration of an element. Each change in atomic number across elements signifies a new element with a different electron configuration and chemical properties.

spdf Notation

Electron configurations are expressed using spdf notation, where each letter represents a different type of atomic orbital:

• s: spherical in shape, holding up to 2 electrons.
• p: dumbbell-shaped, can hold up to 6 electrons.
• d: more complex shape, holding up to 10 electrons.
• f: more complex than d, can hold up to 14 electrons.

These letters are paired with numbers that indicate the energy level, and together they provide a complete picture of where electrons are housed. For instance, 1s^2 details two electrons in the first energy level’s s orbital, while 2p^6 describes six electrons in the second energy level’s p orbitals. In sequences, such as the electron configuration of vanadium, this notation helps to determine how electrons are spread across various orbitals.

Orbitals

Orbitals are regions in an atom where electrons are likely to be found. They come in different types and shapes:

• The s orbital is spherical, and each energy level has one s orbital.
• The p orbitals are shaped like dumbbells, existing in sets of three that can take on orientations along different axes.
• The d orbitals are more varied in shape and come in groups of five.
• The f orbitals are even more complex, existing in groups of seven.

Each orbital can hold a specific number of electrons—2 for s, 6 for p, 10 for d, and 14 for f. Understanding the nature of these orbitals and their capacity for electrons is crucial for determining how electrons are arranged in an atom, ultimately influencing chemical behavior and bonding.

Electron Filling Order

When it comes to electron configurations, electrons fill orbitals in a specific order based on their energy levels, often referred to as the Aufbau principle. This order helps chemists predict the arrangement of electrons in atoms. The sequence follows the rule:

• 1s
• 2s
• 2p
• 3s
• 3p
• 4s
• 3d

This progression indicates that certain lower energy orbitals fill before others. For example, the 4s orbital fills before the 3d , even though numerically it might seem backward. Compiling the electrons in this prescribed order ensures that the configuration provides a stable and least energy-intensive arrangement. Understanding this order is key to constructing accurate electron configurations.