Step 1: Hydrogen peroxide \( (\mathrm{H_2O_2}) \) has a bent or skewed structure and is often described as an "open book" because the oxygen atoms and attached hydrogen atoms are not co-planar.
Step 2: In the gas phase, the molecule shows a dihedral angle of around \( 111^\circ \), and in the crystalline state, this angle is about \( 90.2^\circ \). Thus, the statement about a \( 180^\circ \) dihedral angle is incorrect.
Step 3: Bond lengths:
• O–O bond length = 145.8 pm
• O–H bond length = 98.8 pm
These are correct values and confirm options (C) and (D) are correct. Hence, option (B) is false.