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Magazine Chapter 5: Problem 125
Which of these electron configurations are for atoms in the ground state? In excited states? Which are impossible? (a) \(1 s^{2} 2 s^{\prime}\) (b) \(1 s^{2} 2 s^{2} 2 p^{3}\) (c) \([\mathrm{Nc}] 3 s^{2} 3 p^{3} 4 s^{1}\) (d) \([\mathrm{Ne}] 3 s^{2} 3 p^{6} 4 s^{3} 3 d^{2}\) (c) \([\mathrm{Ne}] 3 s^{2} 3 p^{6} 4 f^{4}\) (f) \(1 s^{2} 2 s^{2} 2 p^{4} 3 s^{2}\)
Short Answer
Expert verified
(a) Impossible, (b) Ground state, (c) Excited state, (d) Impossible, (e) Impossible, (f) Excited state.
Step by step solution
01
Understanding Electron Configuration Notation
Electron configurations describe the arrangement of electrons in an atom, assigning electrons to energy levels and subshells. The notation consists of numbers, letters, and superscript numbers where the number refers to the energy level, the letter indicates the type of orbital (s, p, d, f), and the superscript represents the number of electrons in that orbital.
02
Review of Configuration Rules
The electron configuration should follow the Aufbau principle, Pauli exclusion principle, and Hund's rule. The Aufbau principle dictates that electrons fill orbitals starting at the lowest available energy levels before filling higher levels. The Pauli exclusion principle states that no two electrons can have the same set of quantum numbers, implying a limit of two electrons per orbital with opposite spins. Hund's rule tells us that electrons fill degenerate orbitals (of the same energy) singly first before pairing up.
03
Analyzing Configuration (a): 1s虏 2s'
Configuration (a): \(1 s^2 2 s'\) - This configuration is impossible. The \(2s'\) notation is non-standard, as it does not denote a valid orbital or electron count. There must be a numeral as a superscript indicating the number of electrons.
04
Analyzing Configuration (b): 1s虏 2s虏 2p鲁
Configuration (b): \(1 s^2 2 s^2 2 p^3\) - This is a ground state configuration for the nitrogen atom. The total electron count is 7, which matches a neutral nitrogen atom, and all rules of electron configuration are followed.
05
Analyzing Configuration (c): [Ne]3s虏 3p鲁 4s鹿
Configuration (c): \([\text{Ne}] 3s^2 3p^3 4s^1\) - This is an excited state configuration for the phosphorus atom. It has the correct number of electrons (15) but has one electron in the 4s orbital before the 3p subshell is complete.
06
Analyzing Configuration (d): [Ne]3s虏 3p鈦� 4s鲁 3d虏
Configuration (d): \([\text{Ne}] 3s^2 3p^6 4s^3 3d^2\) - This is impossible because the 4s subshell can only hold a maximum of 2 electrons, but it is shown as having 3.
07
Analyzing Configuration (e): [Ne]3s虏 3p鈦� 4f鈦�
Configuration (e): \([\text{Ne}] 3s^2 3p^6 4f^4\) - This configuration is impossible as well because electrons will fill the 4d orbitals before filling 4f, and this configuration skips the entire 3d and 4s subshells after \([\text{Ne}]\) incorrectly.
08
Analyzing Configuration (f): 1s虏 2s虏 2p鈦� 3s虏
Configuration (f): \(1 s^2 2 s^2 2 p^4 3 s^2\) - This configuration is possible and is the excited state for an oxygen atom. It has 10 electrons in total, but the last two should typically be in the 2p orbital for the ground state.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Ground State
The ground state of an atom refers to the lowest energy state possible for its electrons. In this configuration, all electrons reside in the lowest energy orbitals available. Essentially, this is the most stable configuration for an atom under normal conditions.
For example, for nitrogen with the configuration \(1s^2 2s^2 2p^3\), the electrons fill the lowest energy levels first, according to the Aufbau principle and the other rules governing electron configurations.
This particular arrangement is crucial because it ensures that no lower energy state is accessible for the electrons, signifying a stable and balanced atomic structure.
For example, for nitrogen with the configuration \(1s^2 2s^2 2p^3\), the electrons fill the lowest energy levels first, according to the Aufbau principle and the other rules governing electron configurations.
This particular arrangement is crucial because it ensures that no lower energy state is accessible for the electrons, signifying a stable and balanced atomic structure.
- Lowest energy level
- Most stable arrangement
- Electrons occupy the lowest available orbitals
Excited State
An excited state occurs when one or more electrons in an atom have absorbed energy and moved to a higher energy level than they would occupy in the ground state. This shift can happen when the atom gains external energy, such as heat or light.
For instance, phosphorus having an electron configuration of \([Ne] 3s^2 3p^3 4s^1\) is in an excited state. Normally, the 4s orbital would be occupied only after all the 3p orbitals are filled.
The electron has jumped to a higher energy 4s level, reflecting the additional energy absorbed by the atom. This condition is often temporary, as electrons tend to return to the ground state by releasing energy.
For instance, phosphorus having an electron configuration of \([Ne] 3s^2 3p^3 4s^1\) is in an excited state. Normally, the 4s orbital would be occupied only after all the 3p orbitals are filled.
The electron has jumped to a higher energy 4s level, reflecting the additional energy absorbed by the atom. This condition is often temporary, as electrons tend to return to the ground state by releasing energy.
- Higher energy than ground state
- Occurs after absorbing energy
- Electrons occupy higher energy orbitals
Aufbau Principle
The Aufbau Principle comes from the German word meaning 'building up.' It is a set of guidelines for determining the electron configuration of an atom.
According to this principle, electrons fill atomic orbitals starting with the lowest energy level before proceeding to higher ones. This ensures that the atom remains in its most stable state possible.
For example, following this systematic approach, electrons will fill the \(1s\) orbital before the \(2s\) one, then complete the \(2p\) orbitals, continuing to higher energy states progressively. It essentially provides a method to "build up" the electron configuration of an atom from the ground up.
According to this principle, electrons fill atomic orbitals starting with the lowest energy level before proceeding to higher ones. This ensures that the atom remains in its most stable state possible.
For example, following this systematic approach, electrons will fill the \(1s\) orbital before the \(2s\) one, then complete the \(2p\) orbitals, continuing to higher energy states progressively. It essentially provides a method to "build up" the electron configuration of an atom from the ground up.
- Electrons fill lowest energy orbitals first
- Determines electron configuration
- Ensures stability of the atom
Pauli Exclusion Principle
The Pauli Exclusion Principle, formulated by Wolfgang Pauli, states that no two electrons in an atom can have the same set of four quantum numbers. This means that each orbital can hold a maximum of two electrons, each with opposite spins.
This principle explains why electrons fill orbitals in the way they do and highlights the limits of how many electrons can occupy a given space. For instance, the \(1s^2\) orbital can contain at most two electrons: one with spin-up and another with spin-down.
It is a fundamental concept explaining the strict limit on electron placements in atomic orbitals.
This principle explains why electrons fill orbitals in the way they do and highlights the limits of how many electrons can occupy a given space. For instance, the \(1s^2\) orbital can contain at most two electrons: one with spin-up and another with spin-down.
It is a fundamental concept explaining the strict limit on electron placements in atomic orbitals.
- Maximum two electrons per orbital
- Electrons must have opposite spins
- Ensures unique electron arrangement
Hund's Rule
Hund's Rule is an essential principle in electron configuration indicating that every orbital in a subshell is singly occupied before any orbital is doubly occupied. Additionally, all electrons in singly occupied orbitals have the same spin.
This rule explains the distribution of electrons among orbitals of the same energy, ensuring that the energy within an atom's subshell is minimized. By filling each orbital singly first, atoms avoid unnecessary electron-electron repulsions, thus acquiring a more stable arrangement.
An example can be seen in the nitrogen atom, where each \(2p\) orbital is occupied by one electron before any pairing occurs.
This rule explains the distribution of electrons among orbitals of the same energy, ensuring that the energy within an atom's subshell is minimized. By filling each orbital singly first, atoms avoid unnecessary electron-electron repulsions, thus acquiring a more stable arrangement.
An example can be seen in the nitrogen atom, where each \(2p\) orbital is occupied by one electron before any pairing occurs.
- Single occupancy before pairing
- Minimizes energy in subshells
- All electrons have same spin direction
