Which Of The Following Atoms Is Diamagnetic In Its Ground-state

Which Atoms Are Diamagnetic in Their Ground State? A Complete Guide

Understanding the magnetic properties of atoms is a fundamental concept in chemistry and physics, revealing the hidden quantum behavior of electrons. When faced with a multiple-choice question asking "which of the following atoms is diamagnetic in its ground-state," the answer hinges on a single, powerful principle: all electrons must be spin-paired. A diamagnetic atom has no unpaired electrons in its outermost electron shells according to the Aufbau principle, resulting in a weak repulsion to magnetic fields. Conversely, any atom with at least one unpaired electron is paramagnetic and is attracted to magnetic fields. This guide will equip you with the systematic knowledge to identify diamagnetic atoms from any list, moving beyond rote memorization to true comprehension.

The Quantum Foundation: Electron Spin and Pairing

To solve this problem, we must first revisit the quantum nature of electrons. Each electron possesses an intrinsic property called spin, which can be visualized as a tiny magnetic moment. Spin has two possible orientations, conventionally labeled +½ (often called "spin-up") and -½ ("spin-down"). According to the Pauli Exclusion Principle, no two electrons in the same atomic orbital can have the same set of quantum numbers. This means an orbital—a region of space with the highest probability of finding an electron—can hold a maximum of two electrons, and those two electrons must have opposite spins. When two electrons occupy the same orbital with opposite spins, their magnetic moments cancel each other out. This state is called spin pairing.

• An atom where every electron in its ground-state electron configuration is paired in this way is diamagnetic.
• An atom with one or more unpaired electrons is paramagnetic.

Therefore, the core of our task is to write the correct ground-state electron configuration for each atom in question and then count the number of unpaired electrons.

The Step-by-Step Diagnostic Method

Follow this foolproof, four-step process for any atom:

1. Determine the Atomic Number (Z): This tells you the total number of electrons in a neutral atom. For example, Oxygen (O) has Z=8, so a neutral oxygen atom has 8 electrons.
2. Construct the Ground-State Electron Configuration: Use the Aufbau principle (building up), which follows the order of increasing orbital energy: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p, etc. Remember the mnemonic: "1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p." Fill each orbital with two electrons (with opposite spins) before moving to the next, except when dealing with degenerate orbitals (orbitals of the same energy, like the three 2p orbitals).
3. Apply Hund's Rule for Degenerate Orbitals: When filling orbitals of equal energy (p, d, f subshells), electrons occupy empty orbitals singly first, all with parallel spins (same spin direction), to maximize total spin and minimize electron-electron repulsion. Only after each orbital in the subshell has one electron do you begin to pair them up.
4. Count Unpaired Electrons: Visually inspect your final configuration. Orbitals with a single electron (e.g., 2p⁴ would be: ↑, ↑, ↑↓) contain unpaired electrons. Orbitals with two electrons (↑↓) are paired. If your count is zero, the atom is diamagnetic. If it is one or more, the atom is paramagnetic.

Practical Examples: Applying the Method

Let's apply this to common elements often found on such lists.

Example 1: Beryllium (Be, Z=4)

1. Configuration: 1s² 2s².
2. The 1s orbital is full (↑↓). The 2s orbital is also full (↑↓).
3. All 4 electrons are paired.
4. Conclusion: Beryllium is diamagnetic.

Example 2: Nitrogen (N, Z=7)

1. Configuration: 1s² 2s² 2p³.
2. The 1s and 2s are full. For the three degenerate 2p orbitals, Hund's rule applies: each gets one electron before any pairing.
3. The 2p subshell looks like: (↑) (↑) (↑). Three unpaired electrons.
4. Conclusion: Nitrogen is strongly paramagnetic.

Example 3: Oxygen (O, Z=8)

1. Configuration: 1s² 2s² 2p⁴.
2. The 2p subshell has four electrons. Following Hund's rule: first three electrons go into separate orbitals: (↑) (↑) (↑). The fourth electron must pair up in one of these orbitals.
3. The 2p subshell looks like: (↑↓) (↑) (↑

Continuing the application of the diagnostic method to the next atom:

Example 4: Fluorine (F, Z=9)

1. Atomic Number (Z): 9 (neutral fluorine atom has 9 electrons).
2. Ground-State Electron Configuration: 1s² 2s² 2p⁵. (Following the Aufbau principle: 1s fills first, then 2s, then the three 2p orbitals).
3. Applying Hund's Rule for Degenerate Orbitals: The 2p subshell contains 5 electrons. According to Hund's rule, the first three electrons occupy each of the three 2p orbitals singly, all with parallel spins (↑). The fourth electron pairs up in one of these orbitals (↑↓). The fifth electron then pairs up in a different orbital (↑↓), resulting in the configuration: (↑↓) (↑) (↑).
4. Counting Unpaired Electrons: The 2p subshell contains two orbitals with a single electron (↑ and ↑) and one orbital with a paired set (↑↓). Therefore, there are two unpaired electrons in the 2p subshell. The 1s and 2s subshells are fully paired.

Conclusion: Fluorine has two unpaired electrons and is therefore paramagnetic.

Summary of the Method's Application: The step-by-step diagnostic method provides a systematic and reliable way to determine both the ground-state electron configuration and the number of unpaired electrons for any neutral atom. By rigorously following the Aufbau principle, applying Hund's rule to degenerate orbitals, and visually inspecting the final configuration, we can accurately predict magnetic properties (diamagnetic for zero unpaired electrons, paramagnetic for one or more). This approach is essential for understanding atomic structure and chemical behavior.

Example 5: Neon (Ne, Z=10)

1. Atomic Number (Z): 10 (neutral neon atom has 10 electrons).
2. Ground-State Electron Configuration: 1s² 2s² 2p⁶. (The 2p subshell is now fully occupied).
3. Applying Hund's Rule for Degenerate Orbitals: The 2p subshell contains 6 electrons. Following Hund's rule, the first three electrons occupy each of the three 2p orbitals singly, all with parallel spins (↑). The next three electrons pair up in these orbitals (↑↓), resulting in the configuration: (↑↓) (↑↓) (↑↓).
4. Counting Unpaired Electrons: All electrons in the 2p subshell are paired. The 1s and 2s subshells are also fully paired.

Conclusion: Neon has zero unpaired electrons and is therefore diamagnetic.

Conclusion

This diagnostic method offers a clear and structured approach to understanding the electron configuration and magnetic properties of neutral atoms. By systematically applying the Aufbau principle and Hund's rule, one can accurately predict whether an atom will be diamagnetic or paramagnetic. This knowledge is fundamental in various fields of science, including chemistry and physics, as it helps in understanding atomic behavior, bonding, and interactions.

The examples provided—Beryllium, Nitrogen, Oxygen, Fluorine, and Neon—demonstrate the versatility and reliability of this method. Each atom's electron configuration and magnetic properties were determined with precision, highlighting the importance of unpaired electrons in dictating magnetic behavior. As we continue to explore the periodic table, this method serves as a reliable tool for predicting and understanding the intricate details of atomic structure and chemical reactivity.