Problem 34 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct representation for \(\mathrm{d}\) orbital is (a) \((\mathrm{n}-1) \mathrm{d}^{1-9} \mathrm{~ns}^{1}\) (b) \((\mathrm{n}-1) \mathrm{d}^{1-10} \mathrm{~ns}^{1-2}\) (c) \((\mathrm{n}-1) \mathrm{d}^{1-5}\) (d) \((\mathrm{n}-\mathrm{l}) \mathrm{d}^{1-\mathrm{wo}} \mathrm{ns}^{2}\)

Step-by-Step Solution

Answer

The correct representation is option (b): \((n-1) d^{1-10} ns^{1-2}\).

Step 1: Understanding d-Orbital Filling

The d orbital starts filling after the s orbital of the same principal quantum shell. For a given principal quantum number \( n \), the d-orbital is filled between \((n-1)d\) subshell. This means that when discussing electrons in a \( d \)-orbital, the electrons are in the \((n-1)\) shell.

Step 2: Determine Electron Configuration Range

The possible electron configuration for \( d \)-orbitals ranges from \((n-1)d^{1} \) to \((n-1)d^{10} \) due to the fact that a \( d \)-orbital can hold a maximum of 10 electrons.

Step 3: Clarify Additional Electron Distribution in ns Orbital

After \((n-1)d\), the \( ns \) orbital often has electrons. The \( ns \) orbital can hold 1 or 2 electrons based on the atom's position in the periodic table, specifically group-wise.

Step 4: Consider the Provided Options

Examine the options to see which one fits the standard electronic configuration for d-block elements. Based on the standard configuration we discussed, the correct option should include \((n-1)d^{1-10}\) and \(ns^{1-2}\).

Key Concepts

Electron Configuration

Electron configuration is a fundamental concept that explains how electrons are organized in an atom. This organization is crucial in determining the atom's chemical behavior. Electrons occupy atomic orbitals, and their arrangement follows a specific order. The configuration is generally written by listing the subshells (e.g., 1s, 2s, 2p, etc.) in the order they are filled with electrons and showing the number of electrons in each subshell as a superscript. For example, the electron configuration of nitrogen is represented as: 1s² 2s² 2p³.

Understanding electron configuration provides insight into the chemical properties of an element. It helps explain why elements in the same group of the periodic table often exhibit similar behavior. For instance, elements with similar outermost electron configurations tend to have comparable reactivity.

Quantum Numbers

Quantum numbers are like the address for electrons in an atom, detailing their position and energy. There are four quantum numbers:

• The principal quantum number ( ) indicates the main energy level occupied by the electron. It is a positive integer (1, 2, 3, etc.).
• The azimuthal quantum number ( l) describes the subshell or shape of the orbital, with possible values ranging from 0 to -1.
• The magnetic quantum number ( m) specifies the orientation of the orbital in space, determined by the azimuthal quantum number.
• The spin quantum number ( s) indicates the electron's spin, which can either be +1/2 or -1/2.

Each electron in an atom is described by a unique set of these four numbers, allowing us to predict their distribution within an atom and their possible interactions in a chemical reaction.

d-block Elements

The d-block elements, also known as transition metals, reside in the central section of the periodic table. These elements have their last electron entering the d-subshell, hence the name. They are notable for their complex electron configurations that involve filling the d-orbital.

Transition metals display various unique properties like variable oxidation states and magnetic qualities, making them invaluable in industries and biological systems. These properties are largely due to the electrons in the (n-1)d subsystem. Additionally, these elements typically form colored compounds and are often good conductors of electricity. Their versatility in forming complex ions highlights their importance in both structural materials and catalysts.

Subshell Filling Order

The order in which subshells are filled with electrons is known as the subshell filling order. It is crucial in constructing the electron configuration of an atom. According to the Aufbau principle, electrons fill orbitals starting from the lowest energy level to higher ones.

The general sequence follows the order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so forth. It's important to note that the (n-1)d subshell fills after the ns subshell. For example, 3d orbitals begin to fill only after 4s is occupied. This order helps in correctly arranging the electrons in elements, particularly transition metals. Understanding this filling sequence is key to determining the electron configuration and predicting element behavior accurately.