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Do the first two valence electrons in a valence electron pair? If so, what is the molecular geometry of the B atom?

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The first two valance electrons do generally pair because they go into a s orbital which can hold just two electrons.  After the first two, the next few go into p orbitals.  For these, the scatter before pair rule (Hund's rule) applies.
The Boron molecule is just the atom, (a molecule of one atom).   Consequently, the "molecular" geometry is just a sphere.  Boron does has three valence electrons (2 s2 2p ).  The electron cloud cannot be exactly spherical due to the occupied p orbital.   However, this fact has no chemical significance.  For most chemical reactions with Boron, the three valance electrons hybridize to form sigma bonds.