If asked to state the nature of the emergency, just say "zero fuel!"

However, you are not absolved from having to explain the lack of
planning that led up to the "emergency", so be prepared for that.
Experienced pilots tend to push the limits as flight after flight, they
find lift in a particular area or circumstance, so arrive lower and
lower, with fewer options. One day this doesn't work, and now it's
oops!, gotta land in those trees, or that lake, or that military or
airport within class B/C airspace (without prior approval).

-Tom