Here, \\\\(Z= 1\\\\). We can derive the expression for the time period of electron in \\\\(n^{th}\\\\) orbit as\\\\(\\quad T_n = \\displaystyle\\frac{1}{f_n} \\propto n^3\\\\)Hence \\\\(\\displaystyle\\frac{T_1}{T_2} = \\displaystyle\\frac{n_1^3}{n_2^3}\\\\). As \\\\(T_1 = 8T_2\\\\), therefore we get\\\\(\\quad 8 = \\left(\\displaystyle\\frac{n_1}{n_2}\\right)^3 \\Rightarrow n_1 = 2n_2\\\\)Thus, the possible values of \\\\(n_1\\\\) and \\\\(n_2\\\\) are \\\\(n_1 = 2, n_2 = 1; n_1= 4, n_2=2;n_1=6, n_2 = 3\\\\) and so on.