Electronic Configuration Of Atoms And Ions

The E° value for the Mn³⁺/Mn²⁺ couple being more positive than that of Cr³⁺/Cr²⁺ or Fe³⁺/Fe²⁺ can be attributed to electronic configuration changes. This change highlights the special stability associated with the half-filled d-subshell of Mn²⁺. Let's analyze the changes in electronic configurations for these transitions:

Mn³⁺ (d⁴) to Mn²⁺ (d⁵): Manganese goes from a d⁴ to a d⁵ configuration, achieving a half-filled 3d subshell, known for stability due to symmetrical electron distribution.

Cr³⁺ (d³) to Cr²⁺ (d⁴): No special stability is achieved as the d⁴ state is less stable compared to a half-filled or full d-subshell.

Fe³⁺ (d⁵) to Fe²⁺ (d⁶): Iron moves from a half-filled d-subshell to a more than half-filled state, which doesn't provide additional stability.

This analysis demonstrates that the Mn³⁺ to Mn²⁺ transition uniquely benefits from the half-filled d⁵ stability, resulting in a more positive E° value. Therefore, the change in electronic configuration from d⁴ to d⁵ is responsible for the more positive E° value.

The highest number of helium atoms is in:

• 4 mol of helium contains 4 * (6.022 x 10²³) helium atoms.
• 4 u of helium is a very small number of atoms.
• 4 g of helium is equal to 1 mol of helium, which contains 6.022 x 10²³ helium atoms.
• 2.271098 L of helium at STP is approximately 0.1 mol of helium.

Therefore, 4 mol of helium has the highest number of atoms.

Step 1: Identify Diamagnetic Ions

Diamagnetic ions are those that do not have unpaired electrons, meaning their electron configuration is fully paired.

Step 2: Examine the Given Ions

• Ce³⁺: Has 1 unpaired electron, so it is paramagnetic.
• Eu²⁺: Has 7 unpaired electrons, so it is paramagnetic.
• Gd³⁺: Has 7 unpaired electrons, so it is paramagnetic.
• Eu³⁺: Has no unpaired electrons, so it is diamagnetic.
• Ce⁴⁺: Has no unpaired electrons, so it is diamagnetic.
• Yb²⁺: Has no unpaired electrons, so it is diamagnetic.

Step 3: Conclusion

The correct answer is: Option (1): Ce⁴⁺ and Yb²⁺ are diamagnetic.

Step 1: Analyze [Co(NH₃)₆]³⁺

In this complex, Co³⁺ is in a strong field provided by NH₃ (a strong ligand). The strong field causes the pairing of electrons, making the complex diamagnetic.

Step 2: Analyze [CoF₆]³⁻

In this complex, Co³⁺ is in a weak field provided by F⁻ (a weak ligand). The weak field does not cause pairing of electrons, making the complex paramagnetic.

Step 3: Conclude the Statements

• Statement I: True — Both complexes are octahedral but differ in magnetic behavior.
• Statement II: True — [Co(NH₃)₆]³⁺ is diamagnetic, and [CoF₆]³⁻ is paramagnetic.

Conclusion

The correct analysis of the magnetic behavior of the complexes confirms that:

Both Statement I and Statement II are true.Step 1: Analyze [Co(NH₃)₆]³⁺

In this complex, Co³⁺ is in a strong field provided by NH₃ (a strong ligand). The strong field causes the pairing of electrons, making the complex diamagnetic.

Step 2: Analyze [CoF₆]³⁻

In this complex, Co³⁺ is in a weak field provided by F⁻ (a weak ligand). The weak field does not cause pairing of electrons, making the complex paramagnetic.

Step 3: Conclude the Statements

• Statement I: True — Both complexes are octahedral but differ in magnetic behavior.
• Statement II: True — [Co(NH₃)₆]³⁺ is diamagnetic, and [CoF₆]³⁻ is paramagnetic.

Conclusion

The correct analysis of the magnetic behavior of the complexes confirms that: Both Statement I and Statement II are true.

Step 1: Recall the Formula for Magnetic Moment

The spin-only magnetic moment ( ) is given by:

$ is the number of unpaired electrons. The magnetic moment depends only on the number of unpaired electrons in the ion.

Step 2: Analyze the Given Ions

A.

- Has 1 unpaired electron.

- Spin-only magnetic moment:

\)

- Has 4 unpaired electrons.

- Spin-only magnetic moment:

\)

- Has 5 unpaired electrons.

- Spin-only magnetic moment:

\)

- Has 4 unpaired electrons.

- Spin-only magnetic moment:

\)

- Has no unpaired electrons.

- Spin-only magnetic moment:

\) $

Step 3: Compare the Magnetic Moments

• and both have .
• and have different magnetic moments from others.

Step 4: Conclusion

The correct answer is: Option (1) - B and D only, since they have the same spin-only magnetic moment.

Statement I: Ferromagnetism is considered as an extreme form of paramagnetism.

In paramagnetism, the magnetic moments of individual atoms or ions are randomly oriented, but they tend to align with an external magnetic field. In ferromagnetism, there is spontaneous alignment of the magnetic moments, even in the absence of an external field, resulting in a much stronger magnetization.
Therefore, Ferromagnetism is considered as an extreme case of Paramagnetism, making the statement accurate.

Statement II: The number of unpaired electrons in a Cr²⁺ ion (Z = 24) is the same as that of a Nd³⁺ ion (Z = 60).

Cr (Chromium) has an electronic configuration of [Ar] 3d⁵ 4s¹. When it becomes Cr²⁺, it loses the 4s electron and one 3d electron giving [Ar] 3d⁴, resulting in four unpaired electrons.

Nd (Neodymium) has an electronic configuration of [Xe] 4f⁴ 6s². When it becomes Nd³⁺, it loses the two 6s electrons and one 4f electron giving [Xe] 4f³, resulting in three unpaired electrons.

Therefore, the number of unpaired electrons is incorrect.

Statement I is TRUE, statement II is FALSE.