As radioactive decay is first-order kinetichalf-life given is \\\\(1600\\\\) years in \\\\(6400\\\\) no. of half-life isn\\\\(= \\dfrac{6400}{1600}=4\\\\)fraction of element remains after n half life is given by \\\\(=\\dfrac{1}{2^n}\\\\)Hence fraction of radium remains after \\\\(4\\\\) half life\\\\(=\\dfrac{1}{2^4}=\\dfrac{1}{16}\\\\).Option D.