Problem 44 - Master Resource Book in JEE Main Physics

Question

\(\mathrm{O}_{2}\) molecule consists of two oxygen atoms. In the molecule, nuclear force between the nuclei of the two atoms. (a) is not important because nuclear forces are short-ranged (b) is as important as electrostatic force for binding the two atoms. (c) cancels the repulsive electrostatic force between the nuclei (d) is not important because oxygen nucleus have equal number of neutrons and protons.

Step-by-Step Solution

Answer

(a) is not important because nuclear forces are short-ranged.

Step 1: Understanding Molecular Forces

In a molecule like \(O_{2}\), the forces determining the bond between atoms include electromagnetic forces, especially covalent bonding involving the sharing of electrons. Nuclear forces, originating from interactions between nucleons (protons and neutrons), operate at much smaller scales, on the order of femtometers (10^{-15} meters), which is significantly shorter than atomic dimensions.

Step 2: Analyze Short-Range Nuclear Forces

Nuclear forces are effective only at distances comparable to the size of a nucleus and decrease rapidly outside the nucleus. Since the typical bond length in molecules is around 100 picometers (10^{-12} meters), nuclear forces cannot contribute significantly to molecular bonding.

Step 3: Evaluate Each Option

Option (a) claims that nuclear forces are unimportant due to their short range, which is consistent with the initial analysis. Option (b) erroneously suggests nuclear forces compete with electrostatic forces, despite their different range of effectiveness. Option (c) asserts nuclear forces cancel electrostatic repulsion, which is incorrect since they do not act at the necessary distance. Option (d) incorrectly relates nucleon number to the importance of nuclear forces in molecule formation.

Step 4: Conclusion From Analysis

Given the nature of nuclear forces, Option (a) correctly states that these forces are not significant in the context of atomic bonding in molecules like \(O_{2}\). The main bonding mechanism in \(O_{2}\) is via electron sharing, and not via nuclear interactions, which are indeed short-ranged and ineffective at molecular scales.

Key Concepts

Nuclear Forces

Nuclear forces are fundamental interactions that occur between the particles within an atomic nucleus. These forces are incredibly strong, but they only operate over very short distances, typically no more than a few femtometers (1 femtometer = 10^{-15} meters), which is about the size of an atomic nucleus.
Due to their short-range nature, nuclear forces are crucial for holding together the nucleus of an atom but are insignificant at the larger scales required to influence the bonding between two separate atoms, such as in a molecule like \(O_2\).
In the context of molecular chemistry, nuclear forces do not play a direct role in the formation of molecules because the importance of these forces diminishes as the distance between nuclei increases beyond the scale of a typical atomic nucleus. As such, when examining atomic bonding, other forces such as electromagnetic forces become much more relevant.

Electromagnetic Forces

Electromagnetic forces are one of the fundamental forces in nature and play a pivotal role in holding atoms and molecules together. They arise from the interaction between charged particles, such as electrons and protons. This force is much longer-ranged compared to nuclear forces and can operate over distances observed in molecular bonding.
In \(O_2\) and other molecules, electromagnetic forces manifest primarily through two mechanisms:

• **Electrostatic Attraction/Repulsion:** This force occurs due to the attraction between negatively charged electrons and positively charged nuclei, as well as repulsion between like-charged particles such as protons within the nuclei or electrons surrounding different nuclei.
• **Covalent Bonding:** A specific type of electromagnetic attraction, this involves the sharing of electron pairs between atoms. The shared electrons attract the positively charged nuclei of both atoms, effectively binding them together.

Through these mechanisms, electromagnetic forces provide the essential framework for the structure and stability of molecules.

Covalent Bonding

Covalent bonding is a type of strong chemical bond where two atoms share pairs of electrons. This sharing allows each atom to attain a stable electron configuration, often resembling that of noble gases, which are known for their stability.
In the molecular structure of \(O_2\), the two oxygen atoms share two pairs of electrons, forming a double bond. This covalent double bond determines the molecule's properties and stability.
Key characteristics of covalent bonds include:

• **Directionality:** Covalent bonds have specific orientations in space, which means the atoms are arranged in particular shapes or patterns, contributing to the geometrical structure of molecules.
• **Strength and Stability:** Covalent bonds are generally strong, providing molecules with stability and making them resistant to breaking under common physical conditions.
• **Involvement in Molecular Properties:** The nature of covalent bonds significantly influences a molecule's reactivity, phase (solid, liquid, gas), and other chemical properties.

Covalent bonding is fundamental to the structure of organic compounds and many inorganic molecules, facilitating the formation of complex molecular structures through electron sharing.