To determine which statement is incorrect, let's evaluate each option one by one:
- Carbon exhibits negative oxidation states along with +4 and +2:
- Carbon can display oxidation states of +4 (such as in CO2), +2 (such as in CO), and even negative states (like -4 in CH4). This statement is correct.
- CO2 is the most acidic oxide among the dioxides of group 14 elements:
- Carbon dioxide (CO2) is indeed the most acidic oxide compared to the dioxides of other group 14 elements like SiO2, GeO2, etc. This statement is correct.
- Among the isotopes of carbon, \(^{13}\text{C}\) is a radioactive isotope:
- The commonly known isotopes of carbon are \(^{12}\text{C}\), \(^{13}\text{C}\), and \(^{14}\text{C}\). Of these, only \(^{14}\text{C}\) is radioactive. \(^{13}\text{C}\) is a stable, non-radioactive isotope. Therefore, this statement is incorrect.
- Carbon cannot exceed its covalency more than four:
- Carbon has a maximum of four valence electrons, allowing it to form a maximum of four covalent bonds. Hence, it cannot exceed a covalency of four. This statement is correct.
Based on the evaluations above, the incorrect statement is: "Among the isotopes of carbon, \(^{13}\text{C}\) is a radioactive isotope." Hence, the correct answer is the option stating that \(^{13}\text{C}\) is a radioactive isotope since \(^{13}\text{C}\) is actually stable.