Question

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

Short answer

The ground-state electron configurations and atomic orbital diagrams for the elements are as follows: a. Na (Sodium): \(1s^2 \, 2s^2 \, 2p^6 \, 3s^1\), with 1 unpaired electron in the 3s orbital. b. Co (Cobalt): \(1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^7\), with 3 unpaired electrons in the 3d orbitals. c. Kr (Krypton): \(1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \, 4p^6\), with 0 unpaired electrons.

Step-by-step solution

1s orbital

Two electrons, both with paired spins, fill the 1s orbital.

2s orbital

Two electrons, both with paired spins, fill the 2s orbital.

2p orbital

Six electrons fill the 2p orbital with paired spins (two in each of the three orbitals).

3s orbital

One electron with an up-spin fills the 3s orbital. The ground-state electron configuration for Na is: #tag_image#[[1s^2] [2s^2] [2p^6] [3s^1]] In Na, there is 1 unpaired electron in the 3s orbital. #b. Co (Cobalt)# #Step 1: Determine the atomic number# Determine the atomic number of cobalt (Co). The atomic number of Co is 27. Therefore, there are 27 electrons in Co. #Step 2: Apply the aufbau principle# Electron configuration for Co: \[1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^7 \] #Step 3: Draw the atomic orbital diagram#

1s orbital

Two electrons, both with paired spins, fill the 1s orbital.

2s orbital

Two electrons, both with paired spins, fill the 2s orbital.

2p orbital

Six electrons fill the 2p orbital with paired spins (two in each of the three orbitals).

3s orbital

Two electrons, both with paired spins, fill the 3s orbital.

3p orbital

Six electrons fill the 3p orbital with paired spins (two in each of the three orbitals).

4s orbital

Two electrons, both with paired spins, fill the 4s orbital.

3d orbital

Seven electrons fill the 3d orbital. First, five electrons are filled with up-spins in all five d orbitals (according to Hund's rule). Then, the next two electrons will pair with the electrons in two d orbitals. The ground-state electron configuration for Co is: #tag_image#[[1s^2] [2s^2] [2p^6] [3s^2] [3p^6] [4s^2] [3d^7]] In Co, there are 3 unpaired electrons in the 3d orbitals. #c. Kr (Krypton)# #Step 1: Determine the atomic number# Determine the atomic number of krypton (Kr). The atomic number of Kr is 36. Therefore, there are 36 electrons in Kr. #Step 2: Apply the aufbau principle# Electron configuration for Kr: \[1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \, 4p^6\] #Step 3: Draw the atomic orbital diagram#

1s orbital

Two electrons, both with paired spins, fill the 1s orbital.

2s orbital

Two electrons, both with paired spins, fill the 2s orbital.

2p orbital

Six electrons fill the 2p orbital with paired spins (two in each of the three orbitals).

3s orbital

Two electrons, both with paired spins, fill the 3s orbital.

3p orbital

Six electrons fill the 3p orbital with paired spins (two in each of the three orbitals).

4s orbital

Two electrons, both with paired spins, fill the 4s orbital.

3d orbital

Ten electrons fill the 3d orbitals with paired spins (two in each of the five orbitals).

4p orbital

Six electrons fill the 4p orbital with paired spins (two in each of the three orbitals). The ground-state electron configuration for Kr is: #tag_image#[[1s^2] [2s^2] [2p^6] [3s^2] [3p^6] [4s^2] [3d^{10}] [4p^6]] In Kr, there are no unpaired electrons. So, the number of unpaired electrons in each element is: - Na: 1 unpaired electron - Co: 3 unpaired electrons - Kr: 0 unpaired electrons