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Chapter 7: Problem 84

Explain why the ground-state electron configurations of \(\mathrm{Cr}\) and \(\mathrm{Cu}\) are different from what we might expect.

Short Answer

Expert verified
The ground state electron configurations of Chromium (Cr) and Copper (Cu) differ from the expected (as per the Aufbau principle) because of the stability that comes with half-filled (in the case of Chromium) and completely filled (in the case of Copper) sub-levels. Hence, Chromium preferentially adopts the configuration with a half-filled 3d subshell \(\mathrm{[Ar] 4s^1 3d^5}\) and Copper adopts the configuration with a filled 3d subshell \(\mathrm{[Ar] 4s^1 3d^{10}}\).

Step by step solution

01

Understand the Atomic Structure and Electron Configuration

Atomic structure consists of shells, subshells, and orbitals, etc. An electron configuration is a distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. The Aufbau principle indicates how the electron configuration normally packages electrons. An electron always attempts to enter the suborbital with the lowest energy first (1s being the lowest), and then fill progressively subshells of higher energy. However, in some elements, this principle is not strictly followed.
02

Establish the Expected Electron Configuration for Chromium and Copper

The atomic number of Chromium (Cr) is 24, so its normal electron configuration is \(\mathrm{1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^4}\), following from the Aufbau Principle. Similarly, the atomic number of Copper (Cu) is 29, so its normal electron configuration is \(\mathrm{1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^9}\) following from the Aufbau Principle.
03

Explain the Anomalous Electron Configurations

For Chromium, the actual electron configuration is \(\mathrm{1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^5}\), which is contrary to the Aufbau principle. This discrepancy is due to the stability that comes along with half-filled sub-levels, which is why an electron from the 4s orbital has been excited to the 3d orbital. For Copper, the actual electron configuration is \(\mathrm{1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^{10}\), which means that one of the 4s electrons gets excited and fills the 3d orbital. This arrangement is stable because fully filled d orbitals are more stable than partially filled d orbitals.

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Most popular questions from this chapter

Alveoli are the tiny sacs of air in the lungs (see Problem 5.136 ) whose average diameter is \(5.0 \times\) \(10^{-5} \mathrm{~m} .\) Consider an oxygen molecule \(\left(5.3 \times 10^{-26} \mathrm{~kg}\right)\) trapped within a sac. Calculate the uncertainty in the velocity of the oxygen molecule. (Hint: The maximum uncertainty in the position of the molecule is given by the diameter of the sac.)

Explain what is meant by a noble gas core. Write the electron configuration of a xenon core.

Indicate which of the following sets of quantum numbers in an atom are unacceptable and explain why: \((a)\left(1,0, \frac{1}{2}, \frac{1}{2}\right),(b)\left(3,0,0,+\frac{1}{2}\right),(c)\left(2,2,1,+\frac{1}{2}\right)\) (d) \(\left(4,3,-2,+\frac{1}{2}\right),\) (e) (3,2,1,1)

How does de Broglie's hypothesis account for the fact that the energies of the electron in a hydrogen atom are quantized?

Which of the following species has the most unpaired electrons: \(\mathrm{S}^{+}, \mathrm{S},\) or \(\mathrm{S}^{-} ?\) Explain how you arrive at your answer.
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