Problem 72 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct order of radii is (a) \(\mathrm{N}<\mathrm{Be}<\mathrm{B}\) (b) \(\mathrm{F}^{-}<\mathrm{O}^{2-}<\mathrm{N}^{3-}\) (c) \(\mathrm{Na}<\mathrm{Li}<\mathrm{K}\) (d) \(\mathrm{Fe}^{+3}<\mathrm{Fe}^{+2}<\mathrm{Fe}^{+4}\)

Step-by-Step Solution

Answer

The correct order is (b): \(\mathrm{F}^{-}<\mathrm{O}^{2-}<\mathrm{N}^{3-}\).

Step 1: Analyze the Ionization States

Consider the charge on each ion. Higher positive charge results in a smaller radius, while higher negative charge results in a larger radius. In option (d), \(\mathrm{Fe}^{+4}\) would actually have a smaller radius than \(\mathrm{Fe}^{+3}\) and \(\mathrm{Fe}^{+2}\), contradicting the order given.

Step 2: Evaluate Group Trends

Consider elements in the same group, such as \(\mathrm{Na}\), \(\mathrm{Li}\), and \(\mathrm{K}\). As we move down a group, the atomic radius increases due to additional electron shells. Therefore, the order should be \(\mathrm{Li}<\mathrm{Na}<\mathrm{K}\), which contradicts option (c).

Step 3: Review Period Trends

Elements across a period (like \(\mathrm{N}\), \(\mathrm{Be}\), and \(\mathrm{B}\)) typically decrease in size from left to right due to increasing nuclear charge attracting the electron cloud more strongly and no added electron shells. Therefore, option (a)'s order is incorrect.

Step 4: Compare Negative Ions

Negative ions \(\mathrm{F}^{-}\), \(\mathrm{O}^{2-}\), and \(\mathrm{N}^{3-}\) increase in size with more negative charge as electrons are added, increasing electron-electron repulsion and resulting in larger radii. This supports the given order in option (b), where \(\mathrm{F}^{-}<\mathrm{O}^{2-}<\mathrm{N}^{3-}\).

Key Concepts

Atomic Radius

The atomic radius refers to the size of an atom from its nucleus to the outer boundary of its electron cloud. It is a fundamental concept that helps understand many chemical properties. One important aspect of atomic radius is the trend it follows in the periodic table.

• As we move down a group (column) in the periodic table, the atomic radius increases. This is because with each step down, an additional electron shell is added, making the atom larger.
• Conversely, as we move across a period (row) from left to right, the atomic radius generally decreases. This is due to the increasing positive charge of the nucleus, which pulls the electron cloud closer, despite no new shells being added.

Understanding these trends can help predict and explain the chemical behavior of different elements.

Ionization States

Ionization state refers to the charge of an ion, which occurs when an atom gains or loses electrons:

• Positive ions, or cations, form when an atom loses electrons, resulting in a smaller radius since there are fewer electrons to repel each other, and the remaining electrons are held more tightly by the nucleus.
• Negative ions, or anions, form when an atom gains electrons. This increases the electron-electron repulsion within the atom, resulting in a larger radius.

It's important to note that for a given element, the more positive the ion, the smaller the ionic radius, and the more negative the ion, the larger the ionic radius.

Electron Configuration

Electron configuration describes the distribution of electrons in an atom's orbitals. It plays a crucial role in determining the chemical and physical properties of an element.

• Elements are arranged in order of increasing atomic number, which corresponds to the number of protons in the nucleus and also the number of electrons in a neutral atom.
• As electrons are added to the orbitals, they fill the lowest energy levels first, according to the "Aufbau principle." Moreover, electrons will pair up in orbitals only if no empty orbitals of the same energy are available, known as "Hund's rule."

The electron configuration of elements determines how they interact with others, influencing atomic radii, ionization energy, and chemical reactivity.

Group Trends

The periodic table is organized into groups, which are vertical columns that contain elements with similar properties. Understanding group trends is essential for predicting how elements behave chemically.

• Group trends are influenced by the number of energy levels and the outer electron configuration. For example, as we move down a group, elements gain more electron shells, which leads to larger atomic radii.
• Elements in the same group typically have similar chemical properties because they have the same number of electrons in their outermost shell. This influences their reactivity and the types of bonds they form.

For any given group, it's critical to note that while the chemical properties may remain similar, the physical properties such as atomic and ionic radii, ionization energies, and electronegativities will show predictable trends when moving down the group.