Arrange The Following Species By Decreasing Atomic Radii

Arranging species by decreasing atomic radii requires understanding the trends in atomic size within the periodic table and the effects of ionization. Atomic radius generally increases as you move down a group (column) and decreases as you move across a period (row) from left to right. Ionization, the process of gaining or losing electrons, significantly affects the size of an atom or ion. Cations (positive ions) are smaller than their parent atoms because they have lost electrons, decreasing electron-electron repulsion and increasing the effective nuclear charge. Conversely, anions (negative ions) are larger than their parent atoms due to increased electron-electron repulsion and a decreased effective nuclear charge.

Let's explore the key factors influencing atomic radii and then apply this knowledge to arrange a given set of species in order of decreasing size.

Factors Influencing Atomic Radii

Several factors determine the size of an atom or ion. These include:

• Principal Quantum Number (n): The principal quantum number determines the energy level of an electron. Higher values of n indicate that the electron is in a higher energy level and farther from the nucleus, leading to a larger atomic radius.

• Nuclear Charge (Z): The nuclear charge is the number of protons in the nucleus. A higher nuclear charge exerts a stronger attractive force on the electrons, pulling them closer to the nucleus and decreasing the atomic radius.

• Effective Nuclear Charge (Zeff): The effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom. It's less than the actual nuclear charge due to the shielding effect of inner electrons. The higher the effective nuclear charge, the smaller the atomic radius.

• Shielding Effect: Inner electrons shield outer electrons from the full nuclear charge. This reduces the attractive force experienced by the outer electrons, causing them to be farther from the nucleus and increasing the atomic radius.

• Electron-Electron Repulsion: Electrons repel each other. This repulsion contributes to the overall size of the electron cloud.

Trends in Atomic Radii in the Periodic Table

The periodic table provides a framework for understanding the trends in atomic radii:

• Down a Group: Atomic radius increases as you move down a group. This is primarily due to the increasing principal quantum number (n). Each successive element in a group has electrons in a higher energy level, which are farther from the nucleus. The shielding effect also contributes to this trend, as the number of inner electrons increases, reducing the effective nuclear charge experienced by the outer electrons.

• Across a Period: Atomic radius decreases as you move across a period from left to right. This is primarily due to the increasing nuclear charge (Z). As the number of protons increases, the attractive force on the electrons becomes stronger, pulling them closer to the nucleus. Although the number of electrons also increases, they are added to the same energy level, so the shielding effect does not significantly increase. The effective nuclear charge increases, leading to a smaller atomic radius.

The Impact of Ionization on Atomic Radii

Ionization, the process of forming ions by gaining or losing electrons, has a significant impact on atomic radii:

• Cations (Positive Ions): Cations are smaller than their parent atoms. When an atom loses electrons to form a cation, it loses its outermost electrons, which are farthest from the nucleus. This reduces electron-electron repulsion and increases the effective nuclear charge, pulling the remaining electrons closer to the nucleus. The greater the positive charge, the smaller the ionic radius. For example, Al³⁺ is smaller than Al²⁺, which is smaller than Al⁺, which is smaller than Al.

• Anions (Negative Ions): Anions are larger than their parent atoms. When an atom gains electrons to form an anion, the increased number of electrons increases electron-electron repulsion. This causes the electron cloud to expand, increasing the ionic radius. The greater the negative charge, the larger the ionic radius. For example, O^2- is larger than O^-, which is larger than O.

• Isoelectronic Species: Isoelectronic species are atoms or ions that have the same number of electrons. For isoelectronic species, the atomic or ionic radius decreases as the nuclear charge increases. This is because a greater nuclear charge exerts a stronger attractive force on the electrons, pulling them closer to the nucleus. For example, consider the isoelectronic series: O^2-, F^-, Ne, Na⁺, Mg²⁺, and Al³⁺. All of these species have 10 electrons, but their nuclear charges are different (8, 9, 10, 11, 12, and 13, respectively). The ionic/atomic radius decreases in the order: O^2- > F^- > Ne > Na⁺ > Mg²⁺ > Al³⁺.

Steps to Arrange Species by Decreasing Atomic Radii

To arrange a set of species by decreasing atomic radii, follow these steps:

1. Identify the Elements: Determine the elements involved in the given species.

2. Locate the Elements on the Periodic Table: Find the positions of the elements on the periodic table. This will help you understand their relative sizes based on periodic trends.

3. Consider the Number of Protons (Nuclear Charge): Note the number of protons in each atom or ion. This is especially important for isoelectronic species.

4. Determine the Number of Electrons: Determine the number of electrons in each atom or ion. This will help you identify if the species are isoelectronic and understand the effect of ionization.

5. Apply Periodic Trends:

   • Elements lower in a group generally have larger atomic radii.
   • Elements to the left in a period generally have larger atomic radii.

6. Consider Ionization Effects:

   • Cations are smaller than their parent atoms. The greater the positive charge, the smaller the ion.
   • Anions are larger than their parent atoms. The greater the negative charge, the larger the ion.

7. Compare Isoelectronic Species: For isoelectronic species, the species with the larger nuclear charge will have the smaller radius.

8. Arrange in Decreasing Order: Based on the above considerations, arrange the species in decreasing order of atomic/ionic radii.

Examples of Arranging Species by Decreasing Atomic Radii

Let's illustrate the process with a few examples.

Example 1: Arrange K, K⁺, Cl, Cl^- in decreasing order of atomic/ionic radii.

1. Elements: Potassium (K) and Chlorine (Cl).

2. Periodic Table: K is in Group 1 (alkali metals) and Period 4. Cl is in Group 17 (halogens) and Period 3.

3. Number of Protons: K has 19 protons, and Cl has 17 protons.

4. Number of Electrons:

   • K has 19 electrons.
   • K⁺ has 18 electrons.
   • Cl has 17 electrons.
   • Cl^- has 18 electrons.

5. Periodic Trends: K is larger than Cl because it is located further to the left in the periodic table (although it is in a later period, the effect of being an alkali metal outweighs being one period later).

6. Ionization Effects:

   • K⁺ is smaller than K because it has lost an electron.
   • Cl^- is larger than Cl because it has gained an electron.

7. Comparing Isoelectronic Species: K⁺ and Cl^- are isoelectronic (both have 18 electrons). K⁺ has a greater nuclear charge (19) than Cl^- (17), so K⁺ is smaller than Cl^-.

8. Decreasing Order: The order of decreasing atomic/ionic radii is: Cl^- > K > K⁺.

Example 2: Arrange Mg, Mg²⁺, O, O^2- in decreasing order of atomic/ionic radii.

1. Elements: Magnesium (Mg) and Oxygen (O).

2. Periodic Table: Mg is in Group 2 (alkaline earth metals) and Period 3. O is in Group 16 (chalcogens) and Period 2.

3. Number of Protons: Mg has 12 protons, and O has 8 protons.

4. Number of Electrons:

   • Mg has 12 electrons.
   • Mg²⁺ has 10 electrons.
   • O has 8 electrons.
   • O^2- has 10 electrons.

5. Periodic Trends: Mg is larger than O because it is located further to the left in the periodic table (and one period later).

6. Ionization Effects:

   • Mg²⁺ is smaller than Mg because it has lost two electrons.
   • O^2- is larger than O because it has gained two electrons.

7. Comparing Isoelectronic Species: Mg²⁺ and O^2- are isoelectronic (both have 10 electrons). Mg²⁺ has a greater nuclear charge (12) than O^2- (8), so Mg²⁺ is smaller than O^2-.

8. Decreasing Order: The order of decreasing atomic/ionic radii is: O^2- > Mg > Mg²⁺.

Example 3: Arrange Na⁺, F^-, Mg²⁺, O^2- in decreasing order of atomic/ionic radii.

1. Elements: Sodium (Na), Fluorine (F), Magnesium (Mg), and Oxygen (O).

2. Periodic Table: Na is in Group 1 and Period 3, F is in Group 17 and Period 2, Mg is in Group 2 and Period 3, O is in Group 16 and Period 2.

3. Number of Protons: Na has 11 protons, F has 9 protons, Mg has 12 protons, and O has 8 protons.

4. Number of Electrons:

   • Na⁺ has 10 electrons.
   • F^- has 10 electrons.
   • Mg²⁺ has 10 electrons.
   • O^2- has 10 electrons.

5. Ionization Effects and Isoelectronic Series: All four species are isoelectronic, having 10 electrons each. Therefore, the size is determined by the nuclear charge. A larger nuclear charge results in a smaller ionic radius.

6. Comparing Isoelectronic Species: Comparing the nuclear charges:

   • O^2- has 8 protons.
   • F^- has 9 protons.
   • Na⁺ has 11 protons.
   • Mg²⁺ has 12 protons.

7. Decreasing Order: Based on increasing nuclear charge, the order of decreasing ionic radii is: O^2- > F^- > Na⁺ > Mg²⁺.

Example 4: Arrange Rb, Mg, Si, Ge in decreasing order of atomic radii.

1. Elements: Rubidium (Rb), Magnesium (Mg), Silicon (Si), and Germanium (Ge).

2. Periodic Table:

   • Rb is in Group 1 (alkali metals) and Period 5.
   • Mg is in Group 2 (alkaline earth metals) and Period 3.
   • Si is in Group 14 and Period 3.
   • Ge is in Group 14 and Period 4.

3. Trends:

   • Rb is largest because it's furthest down and to the left.
   • Ge is larger than Mg and Si because it is in Period 4, while Mg and Si are in Period 3.
   • Between Mg and Si, Mg is larger because it's to the left of Si in Period 3.

4. Decreasing Order: The order of decreasing atomic radii is: Rb > Ge > Mg > Si.

Conclusion

Arranging species by decreasing atomic radii involves understanding the interplay of periodic trends and ionization effects. By considering the principal quantum number, nuclear charge, effective nuclear charge, shielding effect, and electron-electron repulsion, one can accurately predict and arrange the relative sizes of atoms and ions. Specifically, remember that atomic radius increases down a group and decreases across a period. Cations are smaller than their parent atoms, and anions are larger. For isoelectronic species, the species with the highest nuclear charge will be the smallest. These concepts are crucial in understanding and predicting various chemical properties and behaviors. By following the steps outlined above and carefully considering the factors influencing atomic radii, you can confidently arrange any set of species in decreasing order of their atomic or ionic sizes.