Question

Which of the following species will have the largest and the smallest sizes respectively? Na, Mg, $Na^{+}$, $Mg^{2+}$

• A. Mg and $Na^{+}$
• B. Mg and $Mg^{2+}$
• C. Na and $Mg^{2+}$
• D. Na and Mg
• E. $Na^{+}$ and Mg

Hint:

Cation size decreases as positive charge increases.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This question asks us to compare the atomic and ionic radii of sodium (Na) and magnesium (Mg) and their respective cations. The size of an atom or ion is influenced by the number of electron shells, the nuclear charge, and the number of electrons.
Step 2: Key Formula or Approach:
We will use the following periodic trends and principles: 1. Across a Period: Atomic size generally decreases from left to right across a period because the nuclear charge increases while the number of electron shells remains the same, pulling the electrons in more tightly. 2. Cations vs. Neutral Atoms: Cations (positive ions) are always smaller than their parent neutral atoms. This is because they have lost one or more electrons, reducing electron-electron repulsion and often losing an entire electron shell. The remaining electrons are also pulled more tightly by the unchanged nuclear charge. 3. Isoelectronic Species: For isoelectronic species (ions with the same number of electrons), the one with the higher nuclear charge (more protons) will be smaller because it pulls the electron cloud in more strongly. Step 3: Detailed Explanation:
The species we need to compare are Na, Mg, Na\(^+\), and Mg\(^{2+}\). - Na: Atomic number 11 (11 protons, 11 electrons). Electron config: [Ne] 3s\(^1\). - Mg: Atomic number 12 (12 protons, 12 electrons). Electron config: [Ne] 3s\(^2\). - Na\(^+\): 11 protons, 10 electrons. Electron config: [Ne]. - Mg\(^{2+}\): 12 protons, 10 electrons. Electron config: [Ne]. Comparing the Largest Size: - Both Na and Mg are neutral atoms with 3 electron shells. Their ions, Na\(^+\) and Mg\(^{2+}\), have only 2 electron shells. Therefore, the neutral atoms will be larger than the ions. - Now, compare Na and Mg. They are in the same period (Period 3). Moving from Na to Mg (left to right), the atomic radius decreases because Mg has a higher nuclear charge (+12) than Na (+11) pulling on the same number of shells. - Therefore, Na is the largest species among the four. Comparing the Smallest Size: - We need to compare the ions Na\(^+\) and Mg\(^{2+}\). - Both Na\(^+\) and Mg\(^{2+}\) are isoelectronic; they both have 10 electrons with the electron configuration of Neon. - However, Mg\(^{2+}\) has a nuclear charge of +12, while Na\(^+\) has a nuclear charge of +11. - The stronger nuclear charge of Mg\(^{2+}\) pulls the 10 electrons in more tightly than the nucleus of Na\(^+\). - Therefore, Mg\(^{2+}\) is the smallest species among the four. Step 4: Final Answer:
The largest species is Na and the smallest species is Mg\(^{2+}\).