Problem 80 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following statement(s) are correct? (1) the electronic configuration of \(\mathrm{Cr}\) is \([\mathrm{Ar}] 3 \mathrm{~d}^{5} 4 \mathrm{~s}^{1}\) (atomic number of \(\mathrm{Cr}=24\) ) (2) the magnetic quantum number may have a negative value (3) in silver atom, 23 electrons have a spin of one type and 24 of the opposite type (atomic number of \(\mathrm{Ag}=47\) ) (4) the oxidation state of nitrogen in HN, is \(-3\) (a) \(1,2,3\) (b) \(2,3,4\) (c) 3,4 (d) \(1,2,4\)

Step-by-Step Solution

Answer

The correct option is (d) 1, 2, 4.

Step 1: Analyze Chromium's Electron Configuration

The atomic number of Chromium (Cr) is 24. The standard electron configuration for Chromium deviates from the expected \( [\mathrm{Ar}] 3d^4 4s^2 \) due to electron stability considerations. Rather, Chromium is \( [\mathrm{Ar}] 3d^5 4s^1 \), as one electron from the 4s orbital is promoted to the 3d orbital to achieve half-filled stability.

Step 2: Evaluate Magnetic Quantum Number

The magnetic quantum number (m) can range from \(-l \) to \(+l \), where \( l \) is the azimuthal quantum number. Therefore, it is indeed possible for the magnetic quantum number to have negative values.

Step 3: Verify Electron Spin in Silver Atom

Silver (Ag) has an atomic number of 47. Based on the Aufbau principle and the Pauli exclusion principle, it fills up to \( [\mathrm{Kr}] 4d^{10} 5s^1 \). This means it has 10 paired electrons in the 4d orbitals (20 electrons with opposite spins), and 1 unpaired electron in the 5s orbital. Thus, 23 electrons will have one spin type and 24 the opposite type (due to full d-orbitals), confirming the statement.

Step 4: Calculate Nitrogen's Oxidation State in NH3

The ammonia molecule (NH₃) consists of nitrogen and hydrogen. In general, hydrogen has an oxidation state of \( +1 \). Therefore, for the molecule NH₃ to have a net charge of 0, and given that there are three hydrogen atoms, nitrogen must have an oxidation state of \(-3 \) to balance the three \( +1 \) contributions from hydrogen.

Step 5: Determine Correct Statements

From Steps 1-4: - Statement 1 is correct regarding the configuration of Chromium. - Statement 2 is correct about the magnetic quantum number. - Statement 3 is correct for electron spins in the silver atom. - Statement 4 correctly identifies nitrogen's oxidation in NH₃. Thus, the true statements are 1, 2, and 4.

Key Concepts

Electronic Configuration

An atom's electronic configuration outlines how electrons are distributed across atomic orbitals. Understanding this concept is key to grasping elements' chemical behavior and their properties.
Each atom has a unique configuration that follows the Aufbau principle, which states that electrons occupy orbitals starting from the lowest energy to higher ones.
The configuration can be different for specific cases to achieve maximum stability, like in the case of Chromium (Cr), where instead of \([\mathrm{Ar}] 3d^4 4s^2\), the correct configuration is \([\mathrm{Ar}] 3d^5 4s^1\). This shift happens because a "half-filled" \(3d\) subshell provides additional stability. Understanding these exceptions and how electronic configuration works provides insights into the chemical and physical properties of elements.

Oxidation States

Oxidation states help us track electron transfer in chemical reactions, especially in redox reactions. An oxidation state indicates the degree of oxidation of an atom, showing how many electrons have been lost or gained.
Typically, elements follow specific oxidation states based on their group.

• Oxygen usually has an oxidation state of -2.
• Hydrogen is typically +1.
• Transition metals can have multiple states due to their d electrons.

For example, in ammonia (NH\(_3\)), nitrogen's oxidation state is -3, balancing the three +1 states from the hydrogen atoms to result in a neutral molecule.
The understanding of oxidation states is crucial, especially when studying redox reactions and balancing chemical equations.

Electron Spin

Electron spin is a fundamental property of electrons, like charge or mass. Each electron has a magnetic moment due to its spin, which can be either "up" or "down," commonly denoted as \(+1/2\) or \(-1/2\).
The Pauli exclusion principle states that no two electrons in the same atom can have identical quantum numbers, implying no two can have the same spin within a single orbital.
In the case of silver (Ag), which has an electronic configuration of \([\mathrm{Kr}] 4d^{10} 5s^1\), it is clear that the majority of electrons are paired in the 4d orbitals. This results in an equal distribution of electron spin states across the atom.Understanding electron spin is crucial for comprehending magnetic properties and electron arrangements in chemical bonding.

Transition Metals

Transition metals are located in the middle of the periodic table, encompassing groups 3 through 12. These elements are unique due to their partially filled d orbitals, which contribute to their ability to exhibit various oxidation states and complex ion formations. Key Features:

• Varied oxidation states due to electron exchange in sublevel d.
• Formation of colored compounds results from d-d electron transitions.
• High melting and boiling points due to strong metallic bonding.

A classic example is Chromium (Cr), which can display different oxidation states and exhibit stability with half-filled d orbitals.
Studying transition metals helps to understand their role in catalysis, alloy production, and their overall chemical versatility.