Question

Which of the following electron configurations (a-e) are for atoms in the ground state? In the excited state? Which are impossible? (a) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 1 \mathrm{~d}^{1}\) (b) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4}\) (c) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{1} 2 \mathrm{p}^{7} 3 \mathrm{~s}^{2}\) (d) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 3 \mathrm{~s}^{1} 3 \mathrm{p}^{4}\) (e) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 3 \mathrm{~s}^{2} 3 \mathrm{p}^{6} 4 \mathrm{~s}^{2}\)

Short answer

Question: Determine whether the following electron configurations are ground state, excited state, or impossible configurations: (a) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 1 \mathrm{~d}^{1}\) (b) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4}\) (c) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{1} 2 \mathrm{p}^{7} 3 \mathrm{~s}^{2}\) (d) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 3 \mathrm{~s}^{1} 3 \mathrm{p}^{4}\) (e) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 3 \mathrm{~s}^{2} 3 \mathrm{p}^{6} 4 \mathrm{~s}^{2}\) Answer: (a) Impossible (b) Ground state (c) Impossible (d) Excited state (e) Ground state

Step-by-step solution

(a) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 1 \mathrm{~d}^{1}\)

This configuration is impossible. According to the Aufbau principle, electrons should fill in increasing order of energy levels. There is no 1d orbital; the first d orbital is 3d.

(b) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4}\)

This configuration is in the ground state. Following the Aufbau principle, we fill the orbitals in increasing order of energy which would be: \(1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{4}\). So, the configuration aligns with the principles and is in the ground state.

(c) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{1} 2 \mathrm{p}^{7} 3 \mathrm{~s}^{2}\)

This configuration is impossible. According to the Pauli Exclusion Principle, an orbital can have a maximum of two electrons with opposite spins. The 2p orbital can have a maximum of 6 electrons (2p^{6}), but here it is assigned 7 electrons. Therefore, this configuration is not possible.

(d) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 3 \mathrm{~s}^{1} 3 \mathrm{p}^{4}\)

This configuration is in the excited state. According to the Aufbau principle, the next electron should fill the 2p orbital after filling the 2s orbital. However, in this configuration, an electron has skipped the 2p orbital and jumped to the 3s and 3p orbitals. This indicates an excited state.

(e) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 3 \mathrm{~s}^{2} 3 \mathrm{p}^{6} 4 \mathrm{~s}^{2}\)

This configuration is in the ground state. The Aufbau principle states to fill the orbitals in increasing order of energy, which would be: \(1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2}\). The configuration fits these rules and is in the ground state. #Summary# In conclusion, option (b) and option (e) represent the ground state electron configurations. Option (d) represents an excited state electron configuration. Options (a) and (c) are impossible configurations.