Problem 179 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct set of four quantum numbers for the valence electrons of rubidium atom \((\mathrm{Z}=37)\) is: (a) \(5,1,1, \frac{1}{2}\) (b) \(5,0,1, \frac{1}{2}\) (c) \(5,0,0, \frac{1}{2}\) (d) \(5,1,0, \frac{1}{2}\)

Step-by-Step Solution

Answer

The correct set is (c) \(5,0,0, \frac{1}{2}\).

Step 1: Identify Rubidium's Valence Electron

Rubidium (Rb) has an atomic number of \(37\), which means it has \(37\) electrons. It is located in group \(1\) and period \(5\) of the periodic table. The valence electron for rubidium is in the \(5s\) orbital.

Step 2: Understand Quantum Numbers

Quantum numbers describe the properties of orbitals and the electrons in them. They include the principal quantum number \(n\), azimuthal quantum number \(l\), magnetic quantum number \(m_l\), and spin quantum number \(m_s\).

Step 3: Determine Principal Quantum Number \(n\)

The principal quantum number \(n\) corresponds to the energy level or shell of the electron. For rubidium's valence electron in the \(5s\) orbital, \(n = 5\).

Step 4: Determine Azimuthal Quantum Number \(l\)

The azimuthal quantum number \(l\) defines the shape of the orbital. For an 's' orbital, \(l = 0\).

Step 5: Determine Magnetic Quantum Number \(m_l\)

The magnetic quantum number \(m_l\) represents the orientation of the orbital in space and ranges from \(-l\) to \(+l\). For \(l = 0\) (an 's' orbital), \(m_l = 0\).

Step 6: Determine Spin Quantum Number \(m_s\)

The spin quantum number \(m_s\) describes the electron's spin and can be either \(+\frac{1}{2}\) or \(-\frac{1}{2}\). Typically, electrons are assigned \(+\frac{1}{2}\) unless specified otherwise.

Step 7: Combine Quantum Numbers for Valence Electron

Combine the quantum numbers to describe the valence electron of rubidium: \(n = 5, l = 0, m_l = 0, m_s = +\frac{1}{2}\). This matches option (c).

Key Concepts

Valence Electrons

Valence electrons are the outermost electrons of an atom and play a crucial role in chemical bonding and reactions. They are the electrons located in the last energy shell of an atom. For elements in the main groups of the periodic table, all valence electrons are counted for their ability to engage in forming chemical compounds. In rubidium, which is found in group 1, the lone valence electron is situated in the fifth shell, indicating its position high up in the periodic table. This electron dictates how rubidium will chemically react with other elements.
Understanding valence electrons is key to predicting how an element will bond with others:

• Elements with a similar number of valence electrons are typically grouped together in the same column of the periodic table.
• These electrons determine the element's reactivity, such as metals in group 1, which are highly reactive.

Understanding the concept of valence electrons is foundational for students studying chemistry or anyone with an interest in how atoms interact with one another.

Quantum Mechanics

Quantum mechanics is the framework of physics that describes the behavior of matter and energy at the atomic and subatomic levels. It's important for understanding the structure of atoms and molecules. This field provides the rules for the existence of electrons within atoms, as well as how they fill different energy levels and interact to form chemical bonds. In atoms, electrons behave differently than macroscopic particles, and their properties are described by quantum numbers.
Quantum mechanics is central to understanding fundamental atomic properties:

• The principal quantum number \( n \) indicates the electron's energy level.
• The azimuthal quantum number \( l \), or angular momentum quantum number, describes the shape of the orbital.

These principles are essential for determining the positional behavior of electrons around an atom's nucleus.

Electron Configuration

Electron configuration refers to the arrangement of electrons in an atom's orbitals. This arrangement is crucial, as it dictates an element's chemical properties and its placement in the periodic table. Each electron in an atom is described by a unique set of quantum numbers, and the configuration follows a pecking order governed by the principles of quantum mechanics.
Key insights into electron configuration include:

• The Aufbau Principle, which states electrons fill orbitals starting from the lowest to the highest energy levels.
• Pauli Exclusion Principle, where no two electrons can have the same set of quantum numbers within an atom.
• Hund's Rule, which ensures electrons fill degenerate orbitals with parallel spins before pairing occurs.

Examining electron configuration not only predicts how atoms will interact during reactions, but also explains periodic trends like ionization energy and atomic radii. Mastery of electron configuration enables students to anticipate how elements will behave as they engage in chemical interactions.