91Ó°ÊÓ

To write the electronic configuration of carbon, fill the electrons in the atomic orbitals according to the Aufbau principle (1s, 2s, 2p, 3s, 3p, …). Carbon has 6 electrons, and they will be filled like this: 1s, 2s, 2px, 2py, 2pz. In spectroscopic notation, the notation will look like this: \(1s^{2}, 2s^{2}, 2p^{2}\)

We'll use the following notation for the quantum numbers: (n, l, m) Where n is the principal quantum number, l is the angular momentum quantum number, and m is the magnetic quantum number. 1s: (1, 0, 0) 2s: (2, 0, 0) 2px: (2, 1, -1) 2py: (2, 1, 0) 2pz: (2, 1, 1)

To satisfy the Pauli Exclusion Principle, each orbital can have a maximum of two electrons with opposite spins (+1/2 and -1/2). For each orbital, we'll list both electrons if applicable, and remember that there can be alternative possibilities. Electron 1: (1, 0, 0, +1/2) Electron 2: (1, 0, 0, -1/2) Electron 3: (2, 0, 0, +1/2) Electron 4: (2, 0, 0, -1/2) Electron 5: (2, 1, -1, +1/2) Electron 6: (2, 1, 0, +1/2) or (2, 1, 1, +1/2) In conclusion, the electronic configuration of the ground state of the carbon atom in the spectroscopic notation is \(1 s^{2}, 2 s^{2}, 2 p^{2}\), and the possible quantum numbers for each electron are Electron 1: (1, 0, 0, +1/2), Electron 2: (1, 0, 0, -1/2), Electron 3: (2, 0, 0, +1/2), Electron 4: (2, 0, 0, -1/2), Electron 5: (2, 1, -1, +1/2), Electron 6: (2, 1, 0, +1/2) or (2, 1, 1, +1/2).