Answer: A half-note is the largest note that can fit in one measure on it’s own without any ties to other notes.
2/4 means two beats per measure, no more. So we can’t fit a whole note, or a dotted half-note.
You are allowed to play or write a note as long as you like - but in 2/4, if it exceeds 2 beats you will start needing ties to express how long the note will sustain.
Explanation: hope this helps