alternate / alternative
Taking turns or every other, versus another option.
Use alternative for an option chosen in place of another: an alternative plan, no alternative. Use alternate for what occurs by turns, as a verb (the two chairs alternate) or as an adjective meaning “every other” (alternate Saturdays). Also use it for a standby held ready to serve if the usual person or thing cannot, as a noun (an alternate on the jury) or as an adjective (an alternate delegate).
Alternate names what rotates or what waits in reserve. An option open to choice is an alternative. Using alternate for any option (an alternate plan) is common, but it does not belong in standard English, and many people judge the speaker who uses it. The adverbs divide the same way: alternately means “by turns,” and alternatively means “as another option.” The set phrase alternate reality is the one established exception.
Examples
Use The clinic stays open late on alternate Thursdays.
Use They offered an alternative route.
Use The city marked an alternate route around the closed bridge.
Avoid The town is investing in alternate energy. (Alternate is the error: the town has chosen this energy as an option, not held it in reserve. Write The town is investing in alternative energy.)
Avoid Alternately, you can renew the permit online. (Alternately is the error: alternately means “by turns,” and this sentence offers another option. Write Alternatively, you can renew the permit online.)
Use The novel is set in an alternate reality.
General dictionaries list alternate as a synonym of alternative. The listing records common use; it does not make the use standard.