The number of incomplete orbitals in inner transition elements is?

3

Inner transition elements are a subset of the transition elements, located in the f-block of the periodic table. The f-block elements consist of the lanthanide series (4f series) and the actinide series (5f series). These series of elements have their valence electrons occupying the f-orbitals.

The f-orbital has the capacity to hold a maximum of 14 electrons per energy level. However, in inner transition elements, the f-orbitals are only partially filled. This means that the electrons in the f-orbitals do not completely occupy all the available slots.

In the lanthanide series, for example, the 4f orbitals are being filled. Since there are seven energy levels (n = 4 to n = 10) available for the 4f orbitals, the maximum number of electrons that can be accommodated is 7 x 2 = 14 (due to the Pauli exclusion principle, with each orbital holding a maximum of 2 electrons).

However, in the lanthanide series, the f-orbitals are progressively filled, resulting in a gradual increase in the number of electrons. For example, in the first element of the series, lanthanum (La), there is one electron in the 5d orbital and none in the 4f orbital. But in the last element of the series, lutetium (Lu), there are two electrons in the 5d orbital and nine electrons in the 4f orbital.

Similarly, in the actinide series, the 5f orbitals are being filled. The actinide elements follow a similar pattern as the lanthanide series, with the gradual filling of the 5f orbitals across the series.

Due to the partial filling of the f-orbitals, there are three incomplete orbitals in inner transition elements. These three incomplete f-orbitals represent the number of available slots for electrons in the f-subshell of these elements.

Therefore, the correct answer is (4) 3, indicating that inner transition elements have three incomplete f-orbitals.