Hybridisation is the process of intermixing the orbitals of slightly different energies to form a new set of orbitals of equivalent energies and shapes.
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The ground state electronic configuration of Be is 1s2 2s2 2p1. In the excited state, one of the 2s-electrons is promoted to the vacant 2p orbital.
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One 2s and two 2p-orbital get hybridised to form three sp2 hybridised orbitals. These three sp2 hybrid orbitals are oriented in opposite directions forming an angle of 120°.
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Each of the sp2 hybridised orbital overlaps with the 2p-orbital of fluorine atoms axially and forms two Be-Cl sigma bonds.
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\( \begin{array}{l}{ }_{9}=-\frac{1 l}{2 s} \quad \begin{array}{|c|c|c|}\hline 11 & 1 l & 1 \\ 2 p_{x} & 2 p_{y} & 2 p_{z}\end{array} \\ sp ^{2} \text { hybridisation } \\\end{array} \)