English is a complicated language and some very closely resembling words of English have meanings that are amazingly different from each other. Alternately and alternatively are two words that have only a slight difference in them i.e. –iv after the second t is present in one while absent in other. Generally looking over them will suggest that there isn’t any difference in them but there is.
Alternately as adverb:
Alternatively as adverb:
Maybe the Vietnam War offers some perspective: from 1969 on, the US and North Vietnamese alternately escalated and eased military activity while peace negotiations dragged on and off; the US was especially active in launching massive bomb campaigns to encourage North Vietnam to accept an accord. (The World Post)
The second approach professes that markets are too efficient to allow for “better” indices, and that outperformance can be best obtained by exposure to these very same investment factors — which is not something the makers of alternatively weighted products care to admit. (The Financial Times)
Alternately or alternatively:
Alternately means several things taken in turn, consecutively, one after another. Alternately is an adverb formed by adding -ly to the word alternate, which comes from the Latin word alternatus meaning one after the other. Alternatively means another choice, on the other hand, another possibility. Alternatively is an adverb formed by adding -ly to the word alternative, which also derives from the Latin word alternatus. Remember, alternately refers to several things following each other in turn, alternatively refers to a different, separate option or choice.