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Magazine Chapter 23: Problem 2
Give the ground-state electron configuration for \(\mathrm{Mn}, \mathrm{Mn}^{2+}, \mathrm{Au}, \mathrm{Au}^{3+}, \mathrm{Mo}\), and \(\mathrm{Mo}^{5+}\)
Short Answer
Expert verified
Mn: [Ar] 3d鈦� 4s虏; Mn虏鈦�: [Ar] 3d鈦�; Au: [Xe] 4f鹿鈦� 5d鹿鈦� 6s鹿; Au鲁鈦�: [Xe] 4f鹿鈦� 5d鈦�; Mo: [Kr] 4d鈦� 5s鹿; Mo鈦碘伜: [Kr] 4d虏.
Step by step solution
01
Understand Electron Configuration Basics
Electron configuration describes the distribution of electrons in atomic orbitals. We follow the Aufbau principle: fill from lower to higher energy levels (orbitals). Hund鈥檚 rule and the Pauli exclusion principle help further manage electron distribution within subshells.
02
Determine Electron Configuration of Mn
Manganese (Mn) has an atomic number of 25. Distribute 25 electrons across the energy levels: 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 4s虏 3d鈦�. Hence, the electron configuration of Mn is \[\text{Mn: }\, 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^5.\]
03
Electron Configuration for Mn虏鈦� Ion
When forming the Mn虏鈦� ion, remove two electrons from the outermost shell, starting with the 4s orbital: 3d鈦� remains after \(4s^2\) electrons are removed. Thus, \[ \text{Mn}^{2+}: \, 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 3d^5. \]
04
Determine Electron Configuration of Au
Gold (Au) has an atomic number of 79. Its electron configuration is determined by distributing electrons up to 79: 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 4s虏 3d鹿鈦� 4p鈦� 5s虏 4d鹿鈦� 5p鈦� 6s鹿 4f鹿鈦� 5d鹿鈦�, resulting in: \[ \text{Au: }\, [Xe] \, 4f^{14} \, 5d^{10} \, 6s^1. \]
05
Electron Configuration for Au鲁鈦� Ion
For the Au鲁鈦� ion, remove three electrons from the outer configurations (6s and 5d orbitals): 5d鈦� remains after removing one 6s electron and two from 5d. Thus: \[ \text{Au}^{3+}: \, [Xe] \, 4f^{14} \, 5d^{8}. \]
06
Determine Electron Configuration of Mo
Molybdenum (Mo) has an atomic number of 42. Its electron configuration is: 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 4s虏 3d鹿鈦� 4p鈦� 5s鹿 4d鈦�. Therefore: \[ \text{Mo: }\, [Kr] \, 4d^5 \, 5s^1. \]
07
Electron Configuration for Mo鈦碘伜 Ion
For the Mo鈦碘伜 ion, five electrons are removed from the outermost shells (5s and 4d orbitals): leaving only 4d虏. Thus: \[ \text{Mo}^{5+}: \, [Kr] \, 4d^2. \]
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Atomic Orbitals
Understanding atomic orbitals is key to deciphering electron configurations. Atomic orbitals are regions around an atom鈥檚 nucleus where there is a high probability of finding electrons. Each orbital can hold a maximum of two electrons, which revolve in spaces known as s, p, d, and f orbitals. This helps explain why electrons are arranged in certain predictable patterns around atoms.
- **s orbitals** are spherical and can contain up to 2 electrons.
- **p orbitals** have a dumbbell shape and hold up to 6 electrons spread across three orientations.
- **d orbitals** are more complex, resembling various kinds of clover shapes, and can accommodate 10 electrons across five orientations.
- **f orbitals** are even more intricate, holding up to 14 electrons.
By visualizing how electrons fill these orbitals, you can better understand how chemical elements and ions achieve stability through electron configurations.
- **s orbitals** are spherical and can contain up to 2 electrons.
- **p orbitals** have a dumbbell shape and hold up to 6 electrons spread across three orientations.
- **d orbitals** are more complex, resembling various kinds of clover shapes, and can accommodate 10 electrons across five orientations.
- **f orbitals** are even more intricate, holding up to 14 electrons.
By visualizing how electrons fill these orbitals, you can better understand how chemical elements and ions achieve stability through electron configurations.
Aufbau Principle
The Aufbau principle guides the way in which electron shells are filled in an atom. According to this principle, electrons fill the lowest energy levels first before moving on to higher ones, essentially building up from the bottom. This ensures the most stable electron arrangement within an atom.
- Electrons occupy orbitals in a sequence determined by increasing energy levels: 1s, 2s, 2p, 3s, 3p, and so forth.
- The phrase "n+l rule" is often used, where n is the principal quantum number and l is the azimuthal quantum number. Lower values of (n+l) correspond to lower energy orbitals.
For example, when predicting the electron configuration of Manganese (Mn), the Aufbau principle helps us understand why the electrons fill up as 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 4s虏 3d鈦�, with lower energy orbitals being filled before higher ones take on electrons.
- Electrons occupy orbitals in a sequence determined by increasing energy levels: 1s, 2s, 2p, 3s, 3p, and so forth.
- The phrase "n+l rule" is often used, where n is the principal quantum number and l is the azimuthal quantum number. Lower values of (n+l) correspond to lower energy orbitals.
For example, when predicting the electron configuration of Manganese (Mn), the Aufbau principle helps us understand why the electrons fill up as 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 4s虏 3d鈦�, with lower energy orbitals being filled before higher ones take on electrons.
Hund's Rule
Hund's Rule is a critical concept to understand electron arrangements in subshells. It states that every orbital in a subshell gets one electron each before any orbital gets a second electron. This distribution maximizes the number of electrons with the same spin, contributing to the atom鈥檚 stability.
- Electrons will fill empty orbitals within the same subshell before pairing up.
- This helps reduce electron repulsion within an atom, leading to a lower energy and more stable configuration.
When dealing with an element like Manganese (Mn), Hund鈥檚 Rule explains why the electron configuration within the 3d subshell is 3d鈦�, with one electron in each of the five 3d orbitals, all with parallel spins.
- Electrons will fill empty orbitals within the same subshell before pairing up.
- This helps reduce electron repulsion within an atom, leading to a lower energy and more stable configuration.
When dealing with an element like Manganese (Mn), Hund鈥檚 Rule explains why the electron configuration within the 3d subshell is 3d鈦�, with one electron in each of the five 3d orbitals, all with parallel spins.
Pauli Exclusion Principle
The Pauli Exclusion Principle is one of the cornerstones of quantum mechanics and electron configurations. It mandates that no two electrons can have the same set of four quantum numbers within an atom, essentially meaning each electron must inhabit its unique state.
- This principle ensures that each atomic orbital can accommodate a maximum of two electrons, with opposite spins.
- Spin is a property that describes the intrinsic angular momentum of an electron, important for magnetic properties.
This principle is crucial when figuring out electron configurations, explaining why even at the most preliminary level, like in a helium atom ( 1s虏), the only way to fit two electrons in an s orbital is to have opposite spins.
- This principle ensures that each atomic orbital can accommodate a maximum of two electrons, with opposite spins.
- Spin is a property that describes the intrinsic angular momentum of an electron, important for magnetic properties.
This principle is crucial when figuring out electron configurations, explaining why even at the most preliminary level, like in a helium atom ( 1s虏), the only way to fit two electrons in an s orbital is to have opposite spins.
