Question

fix any errors in these proposed electron configurations.
number of
electrons in
atom proposed electron configuration
10 $1s^{2}1p^{6}2s^{2}$
25 $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{7}$
11 $1s^{4}2s^{4}2p^{3}$

Explanation:

To fix the errors in the proposed electron configurations, we analyze each case based on electron configuration rules (Aufbau principle, Pauli exclusion principle, and Hund's rule):

For 10 electrons:

Step 1: Recall subshell filling order and capacity.

The \(1p\) subshell does not exist (the first \(p\)-subshell is \(2p\)). The correct filling order after \(1s^2\) is \(2s^2\), then \(2p^6\) (since \(2p\) can hold 6 electrons).

Step 2: Calculate total electrons.

\(1s^2 + 2s^2 + 2p^6 = 2 + 2 + 6 = 10\) electrons.
Correct configuration: \(1s^2 2s^2 2p^6\)

For 25 electrons:

Step 1: Recall the Aufbau principle (filling order: \(1s \to 2s \to 2p \to 3s \to 3p \to 4s \to 3d\)).

After \(3p^6\), electrons fill \(4s\) (not \(3d\) directly). The \(4s\) subshell holds 2 electrons before \(3d\) starts.

Step 2: Calculate total electrons with \(4s^2\) included.

\(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^5\) (note: Chromium (\(Z=24\)) and Manganese (\(Z=25\)) have special configurations, but for \(Z=25\), the correct order is \(4s^2\) first, then \(3d^5\) (or \(4s^1 3d^5\) for Cr, but \(Z=25\) is Mn: \(4s^2 3d^5\) is incorrect? Wait, no—\(Z=25\) is Mn: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^5\)? Wait, no: \(4s\) fills before \(3d\), so after \(3p^6\), we fill \(4s^2\), then \(3d^5\) (since \(2 + 2 + 6 + 2 + 6 + 2 + 5 = 25\)). Wait, the proposed configuration missed \(4s^2\).
Correct configuration: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^5\) (or \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^5 4s^2\) is incorrect—order matters: \(4s\) fills first, then \(3d\). So the error is missing \(4s^2\) before \(3d^7\).

For 11 electrons:

Step 1: Recall the Pauli exclusion principle (an \(s\)-subshell can hold at most 2 electrons).

The \(1s\) and \(2s\) subshells are overfilled (\(1s^4\) and \(2s^4\) are invalid; \(s\)-subshells hold 2 electrons max).

Step 2: Apply correct subshell capacities.

Fill \(1s^2\) (2 e⁻), \(2s^2\) (2 e⁻), \(2p^6\) (6 e⁻) → total 10 e⁻. The 11th electron goes to \(3s^1\).
Correct configuration: \(1s^2 2s^2 2p^6 3s^1\)

Summary of Corrections:

Number of Electrons	Proposed Configuration	Error	Correct Configuration
25	\(1s^2 2s^2 2p^6 3s^2 3p^6 3d^7\)	Skipped \(4s^2\) (fills before \(3d\))	\(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^5\) (or \(4s^1 3d^5\) for Cr, but \(Z=25\) is Mn: \(4s^2 3d^5\))
11	\(1s^4 2s^4 2p^3\)	Overfilled \(s\)-subshells; wrong order	\(1s^2 2s^2 2p^6 3s^1\)

(Note: For \(Z=25\), the correct configuration is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^5\) (Manganese), or \(4s^1 3d^5\) is Chromium (\(Z=24\)). The proposed configuration missed \(4s^2\), so adding \(4s^2\) and adjusting \(3d\) to \(5\) (since \(2+2+6+2+6+2+5=25\)) fixes it.)

Answer:

To fix the errors in the proposed electron configurations, we analyze each case based on electron configuration rules (Aufbau principle, Pauli exclusion principle, and Hund's rule):

For 10 electrons:

Step 1: Recall subshell filling order and capacity.

The \(1p\) subshell does not exist (the first \(p\)-subshell is \(2p\)). The correct filling order after \(1s^2\) is \(2s^2\), then \(2p^6\) (since \(2p\) can hold 6 electrons).

Step 2: Calculate total electrons.

\(1s^2 + 2s^2 + 2p^6 = 2 + 2 + 6 = 10\) electrons.
Correct configuration: \(1s^2 2s^2 2p^6\)

For 25 electrons:

Step 1: Recall the Aufbau principle (filling order: \(1s \to 2s \to 2p \to 3s \to 3p \to 4s \to 3d\)).

After \(3p^6\), electrons fill \(4s\) (not \(3d\) directly). The \(4s\) subshell holds 2 electrons before \(3d\) starts.

Step 2: Calculate total electrons with \(4s^2\) included.

\(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^5\) (note: Chromium (\(Z=24\)) and Manganese (\(Z=25\)) have special configurations, but for \(Z=25\), the correct order is \(4s^2\) first, then \(3d^5\) (or \(4s^1 3d^5\) for Cr, but \(Z=25\) is Mn: \(4s^2 3d^5\) is incorrect? Wait, no—\(Z=25\) is Mn: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^5\)? Wait, no: \(4s\) fills before \(3d\), so after \(3p^6\), we fill \(4s^2\), then \(3d^5\) (since \(2 + 2 + 6 + 2 + 6 + 2 + 5 = 25\)). Wait, the proposed configuration missed \(4s^2\).
Correct configuration: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^5\) (or \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^5 4s^2\) is incorrect—order matters: \(4s\) fills first, then \(3d\). So the error is missing \(4s^2\) before \(3d^7\).

For 11 electrons:

Step 1: Recall the Pauli exclusion principle (an \(s\)-subshell can hold at most 2 electrons).

The \(1s\) and \(2s\) subshells are overfilled (\(1s^4\) and \(2s^4\) are invalid; \(s\)-subshells hold 2 electrons max).

Step 2: Apply correct subshell capacities.

Fill \(1s^2\) (2 e⁻), \(2s^2\) (2 e⁻), \(2p^6\) (6 e⁻) → total 10 e⁻. The 11th electron goes to \(3s^1\).
Correct configuration: \(1s^2 2s^2 2p^6 3s^1\)

Summary of Corrections:

Number of Electrons	Proposed Configuration	Error	Correct Configuration
25	\(1s^2 2s^2 2p^6 3s^2 3p^6 3d^7\)	Skipped \(4s^2\) (fills before \(3d\))	\(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^5\) (or \(4s^1 3d^5\) for Cr, but \(Z=25\) is Mn: \(4s^2 3d^5\))
11	\(1s^4 2s^4 2p^3\)	Overfilled \(s\)-subshells; wrong order	\(1s^2 2s^2 2p^6 3s^1\)

(Note: For \(Z=25\), the correct configuration is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^5\) (Manganese), or \(4s^1 3d^5\) is Chromium (\(Z=24\)). The proposed configuration missed \(4s^2\), so adding \(4s^2\) and adjusting \(3d\) to \(5\) (since \(2+2+6+2+6+2+5=25\)) fixes it.)