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The coordination number of a central metal atom in a complex is determined by:
1. The number of only anionic ligands bonded to the metal ion.
2. The number of monodentate ligands around a metal ion bonded by pi-bonds.
3. The number of monodentate ligands around a metal ion bonded by sigma and pi- bonds both.
4. The number of monodentate ligands around a metal ion bonded by sigma bonds.

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Last updated date: 19th Sep 2024
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Hint: For molecules and polyatomic ions the coordination number of an atom is determined by simply counting the other atoms to which it is bonded, by either single or multiple bonds.

Complete Step by step answer: We should first know how to calculate the coordination number of the central metal atom. So the steps are as following:
-First of all identify the central atom in the chemical formula. Most of the time it is transition metal.
-After that locate the atom, molecule, or ion nearest the central metal atom. To do this find the molecule or ion directly beside the metal symbol in the chemical formula of the coordination compound.
-Now add the number of atoms of the nearest atom molecule or ions. You have to note only the number of atoms of that element in the formula. If the central atom is in the middle of the formula, you will need to add up the atoms in the entire molecule.
-Then find the total number of nearest atoms.
So the coordination number of a central metal atom in a complex is determined by the number of ligands around a metal ion bonded by sigma bonds. It is also defined as the number of atoms, ions, or molecules that a central atom or ion holds as its nearest neighbors in a complex.

So according to all this information the correct option is 1st.

Note: In coordination chemistry, a ligand is an ion or molecule (functional group) that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's electron pairs.