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Be is the central atom here. Its electronic configuration is 1s^22s^2, showing two electrons in its valence shell. Two chlorine atoms are bound to it via single covalent bonds. Hence total electron count around the central atom becomes 2+2 = 4 electrons or, two pairs. There is no possibility of a lone pair in the molecule. Hence, according to valence shell electron pair repulsion (VSEPR) calculations, X, the co-ordination number for central atom, should be 2. This implies that the hybridization must be sp; supporting a linear geometry for BeCl2 molecule, with a bond angle of 180 degrees.
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