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Worksheet: Symmetry Operations

Q1:

Which of the following properties is not a prerequisite for symmetry elements within the same symmetry group?

  • AAssociativity ( 𝐴 ( 𝐡 𝐢 ) = ( 𝐴 𝐡 ) 𝐢 .)
  • BClosure (If 𝐴 and 𝐡 belong to the group, and 𝐴 Γ— 𝐡 = 𝐢 , then 𝐢 also belongs to the group.)
  • CIdentity (The symmetry element times its identity, 𝐸 , remains unchanged.)
  • DContinuity (If a molecule contains an 𝑛 axis, then it also contains axes of 𝑛 βˆ’ 1 , 𝑛 βˆ’ 2 , … .)
  • EInverses (There must be an inverse symmetry element that returns the molecule to its original state; 𝐴 Γ— 𝐴 = 𝐸 βˆ’ 1 .)

Q2:

An improper rotation axis, 𝑆 , arises from which of the following situations?

  • ATwo proper rotation axes
  • BA mirror plane and an inversion
  • CA mirror plane and the identity operation
  • DA proper rotation axis and a mirror plane
  • ETwo mirror planes