Chapter 6: Problem 63
What is the maximum number of electrons that can occupy each of the following subshells: (a) \(3 p\), (b) \(5 d\), (c) \(2 s\), (d) \(4 f ?\)
Short Answer
Expert verified
The maximum number of electrons in each subshell is: (a) 3p: 6 electrons, (b) 5d: 10 electrons, (c) 2s: 2 electrons, (d) 4f: 14 electrons.
Step by step solution
01
Determine the quantum number (l) for p orbital
For a p orbital, the azimuthal quantum number l is equal to 1.
02
Apply the formula for maximum electrons in a subshell
To find the maximum electrons in 3p subshell, we use the formula: \(2(2l + 1)\) = \(2(2\times1+1)\) = 6 electrons
#b) Maximum electrons in 5d subshell#
03
Determine the quantum number (l) for d orbital
For a d orbital, the azimuthal quantum number l is equal to 2.
04
Apply the formula for maximum electrons in a subshell
To find the maximum electrons in 5d subshell, we use the formula: \(2(2l + 1)\) = \(2(2\times2+1)\) = 10 electrons
#c) Maximum electrons in 2s subshell#
05
Determine the quantum number (l) for s orbital
For an s orbital, the azimuthal quantum number l is equal to 0.
06
Apply the formula for maximum electrons in a subshell
To find the maximum electrons in 2s subshell, we use the formula: \(2(2l + 1)\) = \(2(2\times0+1)\) = 2 electrons
#d) Maximum electrons in 4f subshell#
07
Determine the quantum number (l) for f orbital
For an f orbital, the azimuthal quantum number l is equal to 3.
08
Apply the formula for maximum electrons in a subshell
To find the maximum electrons in 4f subshell, we use the formula: \(2(2l + 1)\) = \(2(2\times3+1)\) = 14 electrons
In summary, the maximum number of electrons in each subshell is:
(a) 3p: 6 electrons
(b) 5d: 10 electrons
(c) 2s: 2 electrons
(d) 4f: 14 electrons
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Electron Configuration
Electron configuration is a key concept in chemistry that details the arrangement of electrons in an atom's electron shells and subshells. It follows the principle that electrons fill the lowest energy orbitals first, adhering to the Aufbau principle, the Pauli exclusion principle, and Hund's rule.
At its core, the electron configuration forms a unique 'address' for each electron within an atom that includes the energy level, the type of orbital, and the electron's spin. This configuration determines the chemical properties of the element and how it behaves in reactions. For instance, knowing the electron configuration of an element allows us to predict its valency, which is crucial for understanding the formation of chemical bonds.
When considering the maximum electrons in a subshell, as in the exercise above, electron configurations play a vital role. Knowing how to correctly fill subshells is essential for accurately determining the maximum number of electrons that different orbitals can host.
At its core, the electron configuration forms a unique 'address' for each electron within an atom that includes the energy level, the type of orbital, and the electron's spin. This configuration determines the chemical properties of the element and how it behaves in reactions. For instance, knowing the electron configuration of an element allows us to predict its valency, which is crucial for understanding the formation of chemical bonds.
When considering the maximum electrons in a subshell, as in the exercise above, electron configurations play a vital role. Knowing how to correctly fill subshells is essential for accurately determining the maximum number of electrons that different orbitals can host.
Atomic Orbitals
Atomic orbitals are regions around the nucleus of an atom where electrons are likely to be found. Each orbital has a distinct shape and energy associated with it, which contributes to the unique electron configurations of elements. Orbitals are categorized as 's', 'p', 'd', or 'f', with each type having different shapes and capacities to hold electrons.
The 's' orbital is spherical and can contain up to 2 electrons, the 'p' orbital is dumbbell-shaped and can accommodate up to 6 electrons, the 'd' orbital is more complex and holds up to 10 electrons, and the 'f' orbital, being even more complex, can host up to 14 electrons.
The 's' orbital is spherical and can contain up to 2 electrons, the 'p' orbital is dumbbell-shaped and can accommodate up to 6 electrons, the 'd' orbital is more complex and holds up to 10 electrons, and the 'f' orbital, being even more complex, can host up to 14 electrons.
Electron Capacity of Orbitals
- S orbitals: 2 electrons
- P orbitals: 6 electrons
- D orbitals: 10 electrons
- F orbitals: 14 electrons
Azimuthal Quantum Number
The azimuthal quantum number, usually designated by the symbol 'l', is crucial in determining the shape of atomic orbitals and, as a result, the energy levels of electrons. This quantum number defines the subshell and can take on integer values from 0 to n-1, where n is the principal quantum number related to the energy level of the electron.
For example, in the case of 's' orbitals, the azimuthal quantum number is 0, for 'p' orbitals it's 1, for 'd' it's 2, and for 'f' it's 3. This number not only influences the shape but also affects the number of electrons that can occupy a particular subshell, following the formula:
\[ 2(2l + 1) \]
This formula is essential in determining the maximum number of electrons within a subshell, aiding in solving exercises about filling electron subshells as demonstrated in the original problem.
For example, in the case of 's' orbitals, the azimuthal quantum number is 0, for 'p' orbitals it's 1, for 'd' it's 2, and for 'f' it's 3. This number not only influences the shape but also affects the number of electrons that can occupy a particular subshell, following the formula:
\[ 2(2l + 1) \]
This formula is essential in determining the maximum number of electrons within a subshell, aiding in solving exercises about filling electron subshells as demonstrated in the original problem.