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n a molecule having three pairs of electrons around a central atom and a trigonal planar shape, how many lone pairs of electrons does the central atom have?

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Zero, A trigonal planar molecule requires that there are no lone pairs breaking the molecule's parity. This insure that all three atoms exist on the same plane.

What is a molecule?

A group of two or more atoms held together by tempting forces known as chemical bonds; depending on context, the term may or may not add ions which propitiate this criterion is called molecule.

What is an atom?

The smallest unit of ordinary substance forms a chemical element. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms called an atom. Atoms are much small, typically around 100 picometers across.

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