Exercise 1 solution

Rule: one shared pair = 2 electrons, and the bond order is the number of shared pairs.

H2, single bond:  1 pair, bond order 1, 1 x 2 = 2 shared electrons.
O2, double bond:  2 pairs, bond order 2, 2 x 2 = 4 shared electrons.
Cl2, single bond: 1 pair, bond order 1, 1 x 2 = 2 shared electrons.
(The multiplications were run in Python.)

What the pages say:
- H2: the Covalent bond article says "the hydrogen atoms share the two electrons via
  covalent bonding", which is one shared pair. That matches a single bond.
- O2: the Diatomic molecule article says diatomic oxygen has a double bond, and the
  Covalent bond article writes "The bond order is 1+0.5+0.5=2". This is the one
  with the bond order stated outright.
- Cl2: the Diatomic molecule article lists chlorine as a diatomic gas, but the part I
  read does not say what its bond order is. Single is the exercise's own assumption,
  and it fits the usual idea that a halogen atom with seven valence electrons needs
  one more (check, general knowledge).

Check: a double bond is one more shared pair than a single bond, so O2 shares twice
as many electrons as H2 (4 against 2).