I got several peaks within 42-53 ppm in the 13C-NMR diagram. My system contains vinylic carbon atoms. I am suspecting the presence of quarternary carbon in the system. Can I prove the existance quarternary carbon?
One indication that you have a quaternary carbon is the reletive weakness in the signal compared to the other carbon peaks. On way to eliminate the other carbon signals would be to run a DEPT experiment, that way you can see which carbons are primary, secondary, and tertiary, while identifitying quarternary carbons by elimination (they don't appear in DEPT). Hope that helps.
Also, if your can do 2D Heteronuclear Correlation Experiments, the Quaternary Carbon atoms will not have cross peaks with any 1H 13C proton peaks. in one dimension in the other dimension.
If you have enough substance, you could also run a 13C NMR spectrum without 1H-decoupling (or with so-called gated decoupling). A quaternary carbon signal will not show a large (> 120 Hz) splitting due to one-bond C,H spin-spin coupling .