Problem 21 - A Complete Resource Book in Chemistry for JEE Main

Question

Correct order of radii is (a) \(\mathrm{Na}<\mathrm{Li}<\mathrm{K}\) (b) \(\mathrm{N}<\mathrm{Be}<\mathrm{B}\) (c) \(\mathrm{Cf}<\mathrm{S}^{2-}<\mathrm{P}^{3-}\) (d) \(\mathrm{Fe}^{3+}<\mathrm{Fe}^{2+}<\mathrm{Fe}^{4+}\)

Step-by-Step Solution

Answer

Option (a) is correct as K > Na > Li.

Step 1: Identify the Elements and Ions

First, let's identify the elements, ions, or atoms we need to compare. Comparing atoms by their atomic size involves knowing their positions in the periodic table and their charges if they are ions.

Step 2: Periodic Trend Knowledge

Recall that atomic size increases down a group and decreases across a period on the periodic table. This means that within the same group, the element with the higher atomic number will have a larger atomic radius.

Step 3: Evaluate Each Option

Review each option: (a) Na is larger than Li, but K is larger than both (increased size down the group). (b) N is smaller than both Be and B, with B being slightly larger than Be due to increased electron shell. (c) The ionic sizes are S^{2-} < P^{3-} (greater negative charge generally indicates a larger radius), but both are larger than any neutral atom like C. (d) Fe^{3+} < Fe^{2+} < Fe^{4+} does not follow expected ionic size lists (increased positive charge typically means a smaller radius).

Step 4: Select the Correct Option

Compare the elements using the rules above, to narrow down the choices. The correct sequence should reflect how atomic size changes based on electron shell and effective nuclear charge.

Key Concepts

Atomic Radius

Atomic radius refers to the size of an atom, specifically the distance from the center of the nucleus to the boundary of the surrounding cloud of electrons. Understanding atomic radius is crucial because it provides insight into how atoms will interact in a chemical bond.

The periodic table provides us with valuable hints about atomic size trends:

• As you move down a group (column), the atomic radius increases. This increase is due to the addition of electron shells, which makes the outer electrons further from the nucleus.
• When you move across a period (row) from left to right, the atomic radius decreases. In this case, electrons are being added to the same shell, but the positive charge of the nucleus increases, pulling the electrons closer.

These principles help explain why sodium (Na), which is below lithium (Li) in the same group, has a larger atomic radius.
This knowledge is essential when analyzing the problem at hand, as it allows us to predict and rationalize the sizes of elements based on their positions in the periodic table.

Ionic Size

Ionic size is an important aspect when comparing ions, which are atoms with a charge due to the loss or gain of electrons. Ionic radius can differ significantly from atomic radius due to these changes:

• Positively charged ions (cations) are generally smaller than their neutral atoms because the loss of electrons leads to a decrease in electron-electron repulsion and allows the remaining electrons to be pulled closer to the nucleus.
• Negatively charged ions (anions) tend to be larger than their neutral atoms as the addition of electrons increases electron-electron repulsion, causing a spread in the electron cloud.

Consider the problem stated: sulfur in its anion form (S^{2-}) is larger than as a neutral atom. Moreover, the same logic applies when comparing different ions of the same atom. For example, Fe^{3+} is smaller than Fe^{2+} due to its higher positive charge, which leads to a smaller ionic radius as electrons are pulled in more tightly.

Periodic Table

The periodic table is an invaluable tool for understanding the properties of elements and ions, including their atomic and ionic radii. By organizing elements according to their atomic number, the periodic table allows us to observe periodic trends that are fundamental to chemistry.

Here's how to navigate its features to understand size trends:

• Groups: Columns on the periodic table. Elements in the same group often have similar properties, such as increasing atomic size as you descend the group due to added electron shells.
• Periods: Rows across the periodic table. As you move from left to right within a period, elements generally experience an increase in effective nuclear charge, which causes a decrease in atomic size.
• Transition metals and different charge states: Transition metals can have varying ionic sizes depending on their oxidation states, as seen in the exercise with iron ions.

The periodic table is crucial for visualizing and understanding trends like these, casting light on the otherwise complex patterns of atomic and ionic sizes.