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Explain why BeH2 molecule has a zero dipole moment although the Be–H bonds are polar.

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The Lewis structure for BeH2 is as follows: 

There is no lone pair at the central atom (Be) and there are two bond pair. It has a linear structure. Dipole moments of each H–Be bond are equal and are in opposite directions. 

Therefore, they nullify each other and the BeH2 molecule has zero dipole moment.

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