An unanswered constitutional question about the judicial branch involves what?

The answer

One genuinely unanswered constitutional question about the judicial branch involves the meaning of "good behaviour." Article III, Section 1 states that federal judges "shall hold their Offices during good Behaviour" — the clause that gives them what amounts to lifetime tenure. But the Constitution never defines what "good behaviour" actually requires, nor what conduct would forfeit it, nor how any breach short of an impeachable offense would be judged. That ambiguity has never been fully resolved.

In practice, federal judges can only be removed through impeachment by the House and conviction by the Senate for "Treason, Bribery, or other high Crimes and Misdemeanors." So the open question is whether "good behaviour" sets a separate, lower standard for removal than impeachment does, and if so, who would enforce it. That gap between the tenure clause and the impeachment clause has never been settled by practice or by the courts.

Why this is the best answer

Compared with the usual distractors, "good behaviour" is the cleanest example of text the Constitution leaves genuinely undefined:

• "How long justices serve" is not unanswered in the same way — the answer flows directly from the good-behaviour clause: effectively for life, until death, resignation, or impeachment. The undefined part is the standard, not the duration.
• "Whether the Supreme Court exists" is answered plainly: Article III explicitly establishes "one supreme Court."
• "How many justices sit on the Court" is set by Congress, not left mysterious by the Constitution — the number has changed by statute over history.

A related genuine ambiguity: judicial review

Worth knowing for the same exam is that the Constitution never explicitly grants the power of judicial review — the authority to strike down laws as unconstitutional. The Supreme Court claimed that power itself in Marbury v. Madison (1803). Article III also leaves the structure of the lower federal courts largely to Congress: it creates only the Supreme Court and lets Congress "ordain and establish" the inferior courts. These are further places where the framers wrote sparingly and left later generations to fill in the gaps.

The bigger picture

Article III is the shortest of the three branch articles, and its brevity is exactly why it generates open questions. The framers deliberately sketched the judiciary in outline, trusting Congress and the Court to work out the details. The "good behaviour" clause captures this perfectly: it guarantees judicial independence by protecting judges from removal for unpopular rulings, yet by leaving the phrase undefined it also leaves unresolved how a judge who misbehaves — but commits no crime — could ever be held to account.