Question

which diagram is the best representation of the electron energy orbitals for the carbon atom, c, in its ground state (lowest energy state)?

Explanation:

1. Electron Configuration of Carbon: The atomic number of carbon (C) is 6, so it has 6 electrons. The ground - state electron configuration follows the Aufbau principle (filling orbitals in order of increasing energy: \(1s < 2s < 2p < 3s < 3p\cdots\)), Pauli exclusion principle (maximum 2 electrons per orbital with opposite spins), and Hund's rule (electrons in degenerate orbitals (same energy) fill singly first with parallel spins).

• The electron configuration of carbon is \(1s^{2}2s^{2}2p^{2}\).

1. Analyzing Each Diagram:

• Diagram A: The \(2p\) orbitals have one orbital with 2 electrons and the other two \(2p\) orbitals empty. This violates Hund's rule, as electrons in \(2p\) (degenerate orbitals) should fill singly first.
• Diagram B: It shows an electron in the \(3s\) orbital, which is at a higher energy level than \(2p\). Carbon in the ground state should fill \(1s\), \(2s\), and then \(2p\) orbitals before filling \(3s\), so this is an excited state.
• Diagram C:
• The \(1s\) orbital has 2 electrons (paired, following Pauli exclusion principle).
• The \(2s\) orbital has 2 electrons (paired).
• The \(2p\) orbitals: There are two \(2p\) orbitals with one electron each (parallel spins), and one \(2p\) orbital empty. This follows the Aufbau principle (filling \(1s\), \(2s\), then \(2p\)), Pauli exclusion principle (no more than 2 electrons per orbital), and Hund's rule (electrons in \(2p\) orbitals fill singly first). The total number of electrons is \(2 + 2+2=6\) (wait, no, \(1s^{2}\) (2 electrons), \(2s^{2}\) (2 electrons), \(2p^{2}\) (2 electrons) - total 6 electrons. Wait, in the diagram, the \(2p\) orbitals: looking at the diagram, the \(2p\) sub - shell has three orbitals. In the ground state of carbon, two of the \(2p\) orbitals have one electron each (since \(2p^{2}\)), and one is empty. The spins of the electrons in the \(2p\) orbitals are parallel. Also, the \(3s\) and higher orbitals are empty, which is correct for the ground state.
• Diagram D: It shows an electron in the \(3s\) orbital, which is an excited state as electrons should fill lower - energy orbitals first. Also, the filling of \(2p\) orbitals with three electrons (but carbon has only 6 electrons, \(1s^{2}2s^{2}2p^{2}\), so \(2p\) should have 2 electrons) is incorrect.

Answer:

C (the diagram labeled C)