Chapter 3: Problem 30

Which one of the following (a or b) electronic configuration is more stable and why? (a) \(3 \mathrm{~d}^{4} 4 \mathrm{~s}^{2}\) (b) \(3 \mathrm{~d}^{5} 4 \mathrm{~s}^{1}\)

Short Answer

Expert verified

Explain your reasoning. Answer: The electronic configuration (b) \(3 \mathrm{~d}^{5} 4 \mathrm{~s}^{1}\) is more stable because the half-filled d subshell in option (b) provides additional stability compared to configuration (a) \(3 \mathrm{~d}^{4} 4 \mathrm{~s}^{2}\).

Step by step solution

Identify the configurations' orbitals and fillings

For option (a): \(3 \mathrm{~d}^{4} 4 \mathrm{~s}^{2}\), we have d orbitals having 4 electrons, and s orbitals having 2 electrons.\ For option (b): \(3 \mathrm{~d}^{5} 4 \mathrm{~s}^{1}\), we have d orbitals having 5 electrons, and s orbitals having 1 electron.

Check for half-filled or fully-filled subshells

Now let's analyze both options for half-filled and fully-filled subshells stability. (a) In the configuration \(3 \mathrm{~d}^{4} 4 \mathrm{~s}^{2}\), neither subshell is half-filled or fully-filled, thus it doesn't possess any additional stability. (b) In the configuration \(3 \mathrm{~d}^{5} 4 \mathrm{~s}^{1}\), the d subshell has half-filled electronic arrangement, which provides additional stability.

Compare the stability of both configurations

Based on the half-filled and fully-filled subshells, we can now compare the stability of both configurations. Since configuration (b) \(3 \mathrm{~d}^{5} 4 \mathrm{~s}^{1}\) has a half-filled d subshell, it has a higher stability than configuration (a) \(3 \mathrm{~d}^{4} 4 \mathrm{~s}^{2}\).

Conclusion

The electronic configuration (b) \(3 \mathrm{~d}^{5} 4 \mathrm{~s}^{1}\) is more stable than configuration (a) \(3 \mathrm{~d}^{4} 4 \mathrm{~s}^{2}\) because the half-filled d subshell in option (b) provides additional stability.

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Which one of the following (a or b) electronic configuration is more stable and why? (a) \(3 \mathrm{~d}^{4} 4 \mathrm{~s}^{2}\) (b) \(3 \mathrm{~d}^{5} 4 \mathrm{~s}^{1}\)

Short Answer

Step by step solution

Identify the configurations' orbitals and fillings

Check for half-filled or fully-filled subshells

Compare the stability of both configurations

Conclusion

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