Identify the crystalline borax anion

Crystalline borax is sodium tetraborate decahydrate: $\mathrm{Na_2B_4O_7\cdot 10H_2O}$

In the crystalline state, the tetraborate ion is better represented as: $[B_4O_5(OH)_4]^{2-}$

So, the borax crystal contains a tetranuclear borate unit.

Hence, Option A is correct.

Examine the structure of $[B_4O_5(OH)_4]^{2-}$

In this anion:

• Two boron atoms are trigonal planar $\, (sp^2)$
• Two boron atoms are tetrahedral $\, (sp^3)$

Therefore, the number of $sp^2$ and $sp^3$ hybridised boron atoms is equal.

Hence, Option C is correct.

Check whether all boron atoms lie in the same plane

Since two boron atoms are tetrahedral ($sp^3$), the entire set of boron atoms cannot all be coplanar.

Tetrahedral geometry is non-planar, so all boron atoms are not in the same plane.

Hence, Option B is incorrect.

Check the number of terminal hydroxyl groups

The anion is: $[B_4O_5(OH)_4]^{2-}$

There are 4 hydroxyl groups and 4 boron atoms, so effectively there is one terminal hydroxyl group per boron atom.

Hence, Option D is correct.

Final derived answer

Correct options are: $\boxed{A,\ C,\ D}$

Comparison with stored correct answer

Stored correct answer: A, C, D

This matches the derived answer.