Draw atomic orbital diagrams representing the ground-state electron configuration for each of the following elements. a. Na b. Co c. \(\mathrm{Kr}\) How many unpaired electrons are present in each element?

To represent atomic orbital diagrams and ground-state electron configurations, we use the Aufbau principle, Hund's rule, and Pauli's exclusion principle. According to the Aufbau Principle, electrons fill the lowest energy orbitals first, until all electrons have been placed. The order of orbital filling can be determined using the n+l rule. The n+l rule means that we also look at the sum of n (principal quantum number) and l (azimuthal quantum number) of the atomic orbital to decide the order of filling. In short, we fill orbitals in the order 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, and so on. Hund's Rule states that electrons will fill a set of orbitals, like the p or d orbitals, so that they are spread out before they start pairing up. Pauli's Exclusion Principle states that no two electrons in an atom can have the same set of quantum numbers, meaning that they can't be in the same orbital with the same spin.

a. Na (Sodium): The atomic number of Na is 11, which means it has 11 electrons. Using the Aufbau principle: 1s^2 2s^2 2p^6 3s^1 The atomic orbital diagram for Sodium (Na) is: \[ \underset{1s}{\uparrow \downarrow} \underset{2s}{\uparrow \downarrow} \underset{2p}{\uparrow \downarrow \; \uparrow \downarrow \; \uparrow \downarrow} \underset{3s}{\uparrow} \] b. Co (Cobalt): The atomic number of Co is 27, which means it has 27 electrons. Using the Aufbau principle: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^7 The atomic orbital diagram for Cobalt (Co) is: \[ \underset{1s}{\uparrow \downarrow} \underset{2s}{\uparrow \downarrow} \underset{2p}{\uparrow \downarrow \; \uparrow \downarrow \; \uparrow \downarrow} \underset{3s}{\uparrow \downarrow} \] \[ \underset{3p}{\uparrow \downarrow \; \uparrow \downarrow \; \uparrow \downarrow} \underset{4s}{\uparrow \downarrow} \underset{3d}{\uparrow \downarrow \; \uparrow \downarrow \; \uparrow \downarrow \; \uparrow \; \uparrow} \] c. Kr (Krypton): The atomic number of Kr is 36, which means it has 36 electrons. Using the Aufbau principle: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^6 The atomic orbital diagram for Krypton (Kr) is: \[ \underset{1s}{\uparrow \downarrow} \underset{2s}{\uparrow \downarrow} \underset{2p}{\uparrow \downarrow \; \uparrow \downarrow \; \uparrow \downarrow} \underset{3s}{\uparrow \downarrow} \] \[ \underset{3p}{\uparrow \downarrow \; \uparrow \downarrow \; \uparrow \downarrow} \underset{4s}{\uparrow \downarrow} \underset{3d}{\uparrow \downarrow \; \uparrow \downarrow \; \uparrow \downarrow \; \uparrow \downarrow \; \uparrow \downarrow} \] \[ \underset{4p}{\uparrow \downarrow \; \uparrow \downarrow \; \uparrow \downarrow} \]

a. Na (Sodium): Unpaired electrons = 1 b. Co (Cobalt): Unpaired electrons = 3 c. Kr (Krypton): Unpaired electrons = 0 The number of unpaired electrons for each element is: a. Na: 1 b. Co: 3 c. Kr: 0