Give three examples of ions that have an electron configuration of \(n d^{6}(n=3,4,5, \ldots).\)

The electron configuration nd^6 means that there are 6 electrons in the d orbital of the nth energy level. The n value defines the energy level (shell) where the electrons are located, and can be 3, 4, 5, and so on. The d orbital can hold a maximum of 10 electrons.

To find an element that achieves an electron configuration of nd^6 upon losing electrons, we can consider the transition metals, which have electrons in their d orbitals. If we look at the fourth period on the periodic table, we can see Chromium (Cr) with the atomic number 24. Its ground state electron configuration is [Ar] 4s^1 3d^5. If Cr loses 2 electrons (4s^1 and one from the 3d orbital), it forms the Cr2+ ion, which has an electron configuration of 3d^4. As this is not the desired nd^6 configuration, we can move on to the next element in the periodic table. Manganese (Mn) has the atomic number 25, with the ground state electron configuration of [Ar] 4s^2 3d^5. Upon losing two electrons, Mn loses both of its 4s electrons, resulting in the Mn2+ ion with an electron configuration of 3d^5. This is also not the desired configuration. Next, we consider Iron (Fe) with the atomic number 26 and ground state electron configuration of [Ar] 4s^2 3d^6. When Fe loses 2 electrons (both from the 4s orbital), it forms the Fe2+ ion, which has a 3d^6 electron configuration. This is our first example.

To find more examples, we can look at higher periods in the periodic table. In the 5th period, we have the element Tungsten (W) with atomic number 74 and ground state electron configuration of [Xe] 4f^14 5d^4 6s^2. Upon losing 4 electrons (both 6s electrons and two 5d electrons), it forms a W4+ ion, which has the electron configuration of 5d^2. This is not the desired configuration. Rhenium (Re) has the atomic number 75, with ground state electron configuration of [Xe] 4f^14 5d^5 6s^2. Upon losing 1 electron, Re becomes Re1+ with electron configuration of 5d^5, and losing 2 electrons gives Re2+ with electron configuration of [Xe] 4f^14 5d^4. Neither of these match the desired configuration. Next, we check Osmium (Os) with the atomic number 76 and ground state electron configuration of [Xe] 4f^14 5d^6 6s^2. Upon losing 2 electrons (both from the 6s orbital) it forms the Os2+ ion, which has the electron configuration of 5d^6. This is our second example.

Starting from the 6th period, we can check Radon-222 (Rn-222), which has atomic number 86 and ground state electron configuration of [Xe] 4f^14 5d^10 6s^2 6p^6. Upon gaining 4 electrons (filling the 6p orbit and placing 4 more in 6d orbit), the Rn2- ion has an electron configuration of [Xe] 4f^14 5d^10 6s^2 6p^6 6d^4. This is not the desired configuration. Actinium (Ac) with atomic number 89 has the ground state electron configuration of [Rn] 7s^2 6d^1. Upon losing one electron, Ac becomes Ac1+ with electron configuration of [Rn] 7s^1 6d^1. If Ac loses 2 more electrons, it forms the Ac3+ ion with the electron configuration of 6d^1. Neither of these match the desired configuration. Next, we consider Protactinium (Pa) with atomic number 91 and ground state electron configuration of [Rn] 7s^2 5f^2 6d^1. If Pa gains 5 electrons, it will have the electron configuration of [Rn] 5f^7. Losing one electron, however, results in the Pa1+ ion, which has the electron configuration of [Rn] 7s^1 5f^2 6d^1, and after losing two more electrons, we obtain the Pa3+ ion with the electron configuration of 6d^6. This is our third example. Thus, the three ions with electron configurations of the form nd^6 are: 1. Fe2+ (n=3) 2. Os2+ (n=5) 3. Pa3+ (n=6)