Use of ¹⁵N will be inappropriate because method of detection of ³²P and ¹⁵N is different (³²P being a radioactive isotope while ¹⁵N is not radioactive but is the heavier isotope of Nitrogen). Even if ¹⁵N was radioactive then its presence would have been detected both inside the cell (¹⁵N incorporated as nitrogenous base in DNA) as well as in the supernatant because ¹⁵N would also get incorporated in amino group of amino acids in proteins). Hence the use of ¹⁵N would not give any conclusive results.