Problem 27 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following is a diamagnetic ion? (a) \(\mathrm{Cu}^{2+}\) (b) \(\mathrm{Mn}^{2+}\) (c) \(\mathrm{Sc}^{3+}\) (d) \(\mathrm{Co}^{2+}\)

Step-by-Step Solution

Answer

The diamagnetic ion is \( \mathrm{Sc}^{3+} \).

Step 1: Understanding Diamagnetism

Diamagnetism occurs when all the electrons in an ion are paired. This means we have to find the electron configuration of each ion and see if all electrons are paired.

Step 2: Electron Configuration of Cu^{2+}

The electron configuration of Cu (copper) is \[ ext{Cu} : [ ext{Ar}] 3d^{10} 4s^1 \] When it becomes \( ext{Cu}^{2+}\), it loses two electrons, resulting in the configuration \[ ext{Cu}^{2+} : [ ext{Ar}] 3d^9 \] The 3d subshell has 9 electrons, which means there is at least one unpaired electron, making \( ext{Cu}^{2+}\) paramagnetic.

Step 3: Electron Configuration of Mn^{2+}

The electron configuration of Mn (manganese) is \[ ext{Mn} : [ ext{Ar}] 3d^5 4s^2 \] When it becomes \( ext{Mn}^{2+}\), it loses two electrons, resulting in the configuration \[ ext{Mn}^{2+} : [ ext{Ar}] 3d^5 \] The 3d subshell has 5 electrons, which are all unpaired, making \( ext{Mn}^{2+}\) paramagnetic.

Step 4: Electron Configuration of Sc^{3+}

The electron configuration of Sc (scandium) is \[ ext{Sc} : [ ext{Ar}] 3d^1 4s^2 \] When it becomes \( ext{Sc}^{3+}\), it loses three electrons, resulting in the configuration \[ ext{Sc}^{3+} : [ ext{Ar}] \] All electrons are removed from the 3d and 4s subshells, leaving only a filled noble gas core, meaning all electrons are paired, making \( ext{Sc}^{3+}\) diamagnetic.

Step 5: Electron Configuration of Co^{2+}

The electron configuration of Co (cobalt) is \[ ext{Co} : [ ext{Ar}] 3d^7 4s^2 \] When it becomes \( ext{Co}^{2+}\), it loses two electrons, resulting in the configuration \[ ext{Co}^{2+} : [ ext{Ar}] 3d^7 \] The 3d subshell has 7 electrons, which means there are unpaired electrons, making \( ext{Co}^{2+}\) paramagnetic.

Step 6: Conclusion Based on Unpaired Electrons

After analyzing each ion, we conclude that \( ext{Sc}^{3+}\) is diamagnetic because it has no unpaired electrons; it is a completely filled electron configuration up to the noble gas core.

Key Concepts

Electron Configuration

Electron configuration describes the arrangement of electrons in an atom or ion. It's crucial for determining the magnetic properties of an element. Electrons fill subshells in a specific sequence: starting with lower energy levels before moving to higher ones. Each subshell can hold a different number of electrons:

• s-subshell: 2 electrons
• p-subshell: 6 electrons
• d-subshell: 10 electrons
• f-subshell: 14 electrons

When an electron configuration is written, it typically starts with the noble gas that precedes the element in brackets, followed by the order of filling for the outer electrons, like \(\text{[Ar]} 3d^5 4s^2\).
Understanding this helps determine whether an ion is diamagnetic or paramagnetic, based on whether all electrons are paired. For example, in the electron configuration of \(\text{Sc}^{3+}\), \[\text{Sc}^{3+} : [\text{Ar}]\], all electrons beyond the noble gas core are removed, meaning it lacks unpaired electrons, making it diamagnetic.

Paramagnetic Ions

Paramagnetic ions are characterized by having one or more unpaired electrons. These unpaired electrons create magnetic fields that align with external magnetic fields. This causes the ion to be attracted to a magnetic field. In contrast, diamagnetic ions have all their electrons paired, resulting in no net magnetic moment.
To determine if an ion is paramagnetic:

• Write out the electron configuration of the ion.
• Count the number of unpaired electrons in its outer shells.

For instance, \(\text{Mn}^{2+}\) with a configuration of \[\text{Mn}^{2+} : [\text{Ar}] 3d^5\] has five unpaired electrons. Each of these electrons is in its own orbital within the 3d subshell. Consequently, this ion is strongly paramagnetic. Understanding paramagnetism helps in applications that involve magnetic fields, such as MRI machines and certain types of spectroscopy.

Noble Gas Core

The noble gas core simplifies electron configurations by allowing us to abbreviate the part of the configuration that matches the previous noble gas. This is essential because noble gases have completely filled valence shells, providing a stable electron arrangement.
When writing electron configurations, we often start with the symbol of the nearest noble gas, followed by the additional configuration needed to reach the element in question. For example, the noble gas core for cobalt (Co) is argon ([Ar]), so the electron configuration of \(\text{Co}^{2+}\) is written as \[\text{Co}^{2+} : [\text{Ar}] 3d^7\].
Using the noble gas core not only eases writing long configurations but also emphasizes the role of valence electrons in chemical bonding and reactivity. These simplifications are particularly useful when identifying magnetic properties and other chemical behavior linked to electron arrangements.