Question

How many of the following are paramagnetic:
Lu\(^{3+}\), Yb\(^{2+}\), Gd\(^{2+}\), Ce\(^{4+}\), La\(^{3+}\), Zn\(^{2+}\), Cu\(^{2+}\), Mn\(^{2+}\), Sc\(^{3+}\), and Ti\(^{4+}\)

Hint:

Paramagnetism depends on the presence of unpaired electrons. If an atom or ion has unpaired electrons, it will be paramagnetic.

Answer 1

Correct Answer: 3

To determine whether a species is paramagnetic or not, we need to check the number of unpaired electrons. Paramagnetic substances have at least one unpaired electron.
Step 1: Check the electronic configurations and unpaired electrons.
- Lu\(^{3+}\): The electronic configuration of Lu is [Xe] 4f\(^{14}\) 5d\(^{1}\) 6s\(^{2}\). After removing 3 electrons, Lu\(^{3+}\) has a configuration of [Xe] 4f\(^{14}\) 5d\(^{0}\) 6s\(^{0}\). No unpaired electrons, hence not paramagnetic.
- Yb\(^{2+}\): Yb has a configuration of [Xe] 4f\(^{14}\) 6s\(^{2}\). After removing 2 electrons, Yb\(^{2+}\) has [Xe] 4f\(^{14}\), with no unpaired electrons. Hence not paramagnetic.
- Gd\(^{2+}\): Gd has a configuration of [Xe] 4f\(^{7}\) 6s\(^{2}\). After removing 2 electrons, Gd\(^{2+}\) has a configuration of [Xe] 4f\(^{7}\), with 7 unpaired electrons. Paramagnetic.
- Ce\(^{4+}\): Ce has a configuration of [Xe] 4f\(^{1}\) 5d\(^{1}\) 6s\(^{2}\). After removing 4 electrons, Ce\(^{4+}\) has a configuration of [Xe] 4f\(^{0}\), with no unpaired electrons. Hence not paramagnetic.
- La\(^{3+}\): La has a configuration of [Xe] 5d\(^{1}\) 6s\(^{2}\). After removing 3 electrons, La\(^{3+}\) has [Xe] 5d\(^{0}\) 6s\(^{0}\), with no unpaired electrons. Hence not paramagnetic.
- Zn\(^{2+}\): Zn has a configuration of [Ar] 3d\(^{10}\) 4s\(^{2}\). After removing 2 electrons, Zn\(^{2+}\) has [Ar] 3d\(^{10}\), with no unpaired electrons. Hence not paramagnetic.
- Cu\(^{2+}\): Cu has a configuration of [Ar] 3d\(^{10}\) 4s\(^{1}\). After removing 2 electrons, Cu\(^{2+}\) has [Ar] 3d\(^{9}\), with 1 unpaired electron. Paramagnetic.
- Mn\(^{2+}\): Mn has a configuration of [Ar] 3d\(^{5}\) 4s\(^{2}\). After removing 2 electrons, Mn\(^{2+}\) has [Ar] 3d\(^{5}\), with 5 unpaired electrons. Paramagnetic.
- Sc\(^{3+}\): Sc has a configuration of [Ar] 3d\(^{1}\) 4s\(^{2}\). After removing 3 electrons, Sc\(^{3+}\) has [Ar] 3d\(^{0}\), with no unpaired electrons. Hence not paramagnetic.
- Ti\(^{4+}\): Ti has a configuration of [Ar] 3d\(^{2}\) 4s\(^{2}\). After removing 4 electrons, Ti\(^{4+}\) has [Ar] 3d\(^{0}\), with no unpaired electrons. Hence not paramagnetic.

Step 2: Count the paramagnetic species.
From the above analysis, the paramagnetic species are: - Gd\(^{2+}\)
- Cu\(^{2+}\)
- Mn\(^{2+}\)
Thus, the number of paramagnetic species is 3.