State the condition that the wavefunction of a free particle moving in one dimension must satisfy to be normalized.

For a wavefunction to be able to be normalized, the sum of the probability (wavefunction squared) for all values must be equal to 1.

Explain why the anti-periplanar confirmation of dichloroethane is the lowest energy confirmation possible for the molecule.

This is because in this arrangement, the largest atoms (chlorine) are positioned as far away as possible from each other in a staggered arrangement, minimizing steric interaction between the two and lowering overall energy of the molecule.

An electron has a principal quantum number n=4. What are the possible values of the l, and m_l quantum numbers?

l (angular momentum quantum number): 0, 1, 2, 3 m_l (magnetic quantum number): -3, -2, -1, 0, 1, 2, 3