Final answer:
The correct arrangement of electrons in the energy shells of a carbon atom is option 2, with the first energy shell having 2 electrons and the second energy shell having 4 electrons, which corresponds to the electron configuration of 1s² 2s² 2p² for carbon.
Step-by-step explanation:
The arrangement of electrons in the energy shells of a carbon atom can be represented by a Bohr model. Carbon, with an atomic number of 6, has six electrons. According to the Bohr model and quantum mechanics, the electrons fill the lowest available energy levels first. Thus, the first energy shell (1s) holds a maximum of two electrons, and the second energy shell (2s and 2p subshells) will hold the remaining four electrons. Two of these four will fill the 2s subshell completely, and the other two will occupy the 2p subshell, in accordance with Hund's rule, which favors maximum unpaired electrons in degenerate orbitals.
Therefore, the correct option that represents how electrons are arranged in the energy shells of a carbon atom is:
- first energy shell = 2 electrons
- second energy shell = 4 electrons
This corresponds to option 2, as the complete electron configuration for carbon is 1s² 2s² 2p².