alternate(ly), alternative(ly)

The primary meaning of the adjective alternate is “by turns,” “first one, then the other” or “every other one.”

• The nurse and the home care worker come on alternate days.

Alternative refers to one of two (or possibly more) choices.

• Since our first attempt didn’t work, we were forced to try an alternative method.

The same distinction applies to the adverbial forms alternately and alternatively.

• Throughout the trial, Judith was alternately calm and despairing.
• We planned to go by taxi; alternatively, we can take the bus.

Note, however, that alternate can also be used with the meaning of alternative.

• We were forced to try an alternate method.