Final answer:
The correct formula for a lutetium nitrate compound, given lutetium has a +3 charge in both compounds, would be Lu(NO3)3, answer choice e.
Step-by-step explanation:
When writing the formula for a ternary ionic compound, one must consider the charges of the ions to ensure that the compound is electrically neutral. For the lutetium carbonate compound Lu2(CO3)3, lutetium (Lu) must have a +3 charge to balance the three carbonate ions, each with a -2 charge. For lutetium nitrate, given that the charge of lutetium is the same as in the carbonate compound, each Lu3+ would balance with three nitrate (NO3-) ions. Therefore, two lutetium ions would require six nitrate ions to balance the charges. The correct formula for lutetium nitrate would thus be Lu2(NO3)6, or written simplistically: Lu2(NO3)3 following the convention for ionic compounds, which makes choice e. Lu(NO3)3 the correct answer.