The number of cluster electron pairs in [In4Bi5]3- is 11.

Explanation:
A cluster is a group of atoms or ions that are held together by covalent bonds. In the case of [In4Bi5]3-, it is a cluster ion that consists of 4 indium (In) atoms and 5 bismuth (Bi) atoms.

Determining the number of cluster electron pairs involves counting the number of electrons in the cluster and dividing it by two. This is because each covalent bond consists of two electrons, and we are interested in the number of covalent bonds present in the cluster.

To determine the number of electrons in the cluster, we need to consider the electron configuration of the individual atoms. Indium (In) has an atomic number of 49, and its electron configuration is [Kr]5s24d105p1. Bismuth (Bi) has an atomic number of 83, and its electron configuration is [Xe]6s24f145d106p3.

The number of valence electrons in each indium atom is 3 (5s2 and 5p1), while the number of valence electrons in each bismuth atom is 5 (6s2 and 6p3). Therefore, the total number of valence electrons in the cluster is:

4 (number of indium atoms) * 3 (valence electrons per indium atom) + 5 (number of bismuth atoms) * 5 (valence electrons per bismuth atom) = 12 + 25 = 37

Now, dividing this number by two, we get:

37 / 2 = 18.5

Since the number of cluster electron pairs needs to be a whole number, we round down the value to the nearest whole number, which is 18.

However, it is important to note that the cluster ion [In4Bi5]3- carries a charge of -3. This means that there are three extra electrons present in the cluster. These electrons are not involved in covalent bonding and are considered as non-bonding electrons.

Therefore, to find the number of cluster electron pairs, we subtract the number of non-bonding electrons (3) from the total number of electron pairs (18):

18 (total electron pairs) - 3 (non-bonding electrons) = 15

Thus, the number of cluster electron pairs in [In4Bi5]3- is 15.