Problem 66 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct ground state electronic configuration for the atom \((\mathrm{Z}=24)\) is (a) \([\mathrm{Ar}] 3 \mathrm{~d}^{5} 4 \mathrm{~s}^{1}\) (b) \([\mathrm{Ar}] 3 \mathrm{~d}^{4} 4 \mathrm{~s}^{2}\) (c) \([\mathrm{Ar}] 3 \mathrm{~d}^{6} 4 \mathrm{~s}^{0}\) (d) \([\mathrm{Ar}] 3 \mathrm{~d}^{5} 4 \mathrm{~s}^{2}\)

Step-by-Step Solution

Answer

The correct configuration is \([ ext{Ar}] 3d^5 4s^1\) (Option a).

Step 1: Identify the Element

First, determine the element with atomic number \(Z = 24\). From the periodic table, we know that the element with atomic number 24 is Chromium (Cr).

Step 2: Write the Configuration Up to Argon

The neutral atom of Chromium, having \(Z = 24\), uses electrons to fill atomic orbitals starting from the lowest energy level. Starting from Hydrogen, the electron configuration fills up to Argon as follows: \([ ext{Ar}]\). Argon represents 18 electrons.

Step 3: Add Remaining Electrons Post Argon

After Argon's configuration, 6 electrons remain to be accommodated (24 total electrons minus 18 for Argon). Electrons added beyond Argon will be placed in the higher energy orbitals 3d and 4s.

Step 4: Consider the Order of Filling and Aufbau Principle Adjustments

Electrons are typically filled in order of increasing energy level: 3d then 4s. Normally, electrons fill \([Ar] 3d^4 4s^2\), but due to electron-electron interaction and stabilization of half-filled subshells (Hund’s Rule), Chromium instead takes the configuration \([Ar] 3d^5 4s^1\).

Step 5: Select Correct Answer

This electron configuration corresponds to option (a): \([ ext{Ar}] 3d^5 4s^1\).

Key Concepts

Understanding Atomic Number

Every element in the periodic table has a unique atomic number. This number represents the quantity of protons found within an atom's nucleus. It also indicates the number of electrons in a neutral atom. For instance, if the atomic number of Chromium is 24, that signifies it has 24 protons and, in a neutral state, 24 electrons.

• The atomic number is fundamental because it determines the element's identity.
• It's ordered in the periodic table from lowest to highest, revealing the sequence of elements.
• For example, Chromium's position at atomic number 24 helps tell us it's the 24th element on the table and provides a starting point for writing its electronic configuration.

Chromium and Its Unique Configuration

Chromium, with the symbol Cr, exhibits some interesting properties that affect its electron configuration. While general electron filling rules guide it, exceptions like Chromium arise due to stability preferences at the atomic level.

• Chromium's standard configuration is expected to be \([Ar] 3d^4 4s^2\), yet due to a preference for half-filled subshells, it adjusts the arrangement.
• This adjustment means one electron from the 4s orbital jumps to the 3d, leading to \([Ar] 3d^5 4s^1\).
• This unique configuration illustrates how stability can override typical filling sequences.

Hund's Rule and Electron Arrangement

Hund's Rule helps explain how electrons fill orbitals within subshells. The rule is grounded in the principle that atom stability improves when electrons are distributed in a manner where each one has its own orbital, assuming parallel spins, before pairing up.

• This means that, for Chromium's 3d subshell, each of the five d orbitals receives one electron initially.
• This single occupancy minimizes electron repulsion because electrons remain as unpaired as possible.
• It's this action that shifts Chromium's expected electron configuration from \([Ar] 3d^4 4s^2\) to the actual \([Ar] 3d^5 4s^1\).

The Aufbau Principle: Building Electron Configurations

The Aufbau Principle is an essential guideline in determining the electron arrangement of atoms. It suggests that electrons occupy orbitals starting from the lowest energy level, gradually progressing to higher ones. This helps construct the ground state electronic configuration.

• Under typical circumstances, electron filling follows the order of increasing orbital energy: 1s, 2s, 2p, followed by 3s, 3p, then 4s before heading into 3d.
• However, due to specific adjustments, as seen in Chromium, electrons may not strictly follow this order.
• The balance of energy levels and electron exchange stability can prompt deviations to achieve the lowest possible energy state for the atom.