Lanthanides are a group of elements in the periodic table that have atomic numbers ranging from 57 to 71. They are often referred to as rare earth elements and have similar chemical properties. One characteristic of the lanthanides is the ability to exhibit a variety of oxidation states. Among these oxidation states, the II and III states are the most common.

1. Oxidation States of Lanthanides:
Lanthanides typically exhibit an oxidation state of +3, which is the most stable and common oxidation state. This occurs when the lanthanide atom loses three electrons from its outermost energy level. However, some lanthanides can also exhibit an oxidation state of +2, in which the atom loses two electrons. This occurs when the atom loses electrons from both its outermost and second outermost energy levels.

2. Common Lanthanides with II and III Oxidation States:
Among the lanthanides, the II and III oxidation states are most commonly observed in the following elements:

- Europium (Eu): Europium is known to exhibit both the II and III oxidation states. In the +2 state, it loses two electrons from its outermost energy level, while in the +3 state, it loses three electrons. Europium is unique among the lanthanides in this regard.

3. Reason for the Correct Answer:
The correct answer to the question is option B, which states that europium (Eu) is the lanthanide for which II and III oxidation states are common. This is because europium is the only lanthanide that commonly exhibits both the +2 and +3 oxidation states.

In summary, while most lanthanides primarily exhibit an oxidation state of +3, europium is the exception and can exhibit both the +2 and +3 oxidation states. Therefore, the correct answer to the question is option B.