We have empirical and molecular formulae of #C_8H_18O#. We know that there is ONLY the one type of hydrogen nucleus in the structure, so alcohols are out, and thus we deal with a symmetric ether, i.e. #R-O-R#. But within the #R# group, there is only the one type of hydrogen, because the #""^1H# #"NMR spectrum"# yields only the one signal; structures of #(H_3C-CH_2CH_2CH_2)_2O# or #(Pr^iCH_2)_2O# are CONTRAINDICATED in that these would give 4 (or 3) signals in the #""^1H# #NMR#, and 3 signals in the #""^13C{""^1H}# #"NMR spectra"# respectively.
On the other hand, a symmetric structure of #Bu_2^tO#, #(H_3C)_3C-O-C(CH_3)_3# is consistent with the observed data: one signal in the #"proton NMR spectrum"#, and TWO signals in the #""^13C{""^1H}# #"NMR spectrum"#.
