### Application of the Pauli Exclusion Principle in Quantum States #### Hint: Make use of the hint button labeled "HINT" for further guidance on solving these problems. #### Problems: Apply the Pauli exclusion principle to determine the number of electrons that could occupy the quantum states described by the following: 1. **(a) \( n = 4, \ \ell = 3, \ m_\ell = -1 \)** - **Number of Electrons:** [_______] 2. **(b) \( n = 3, \ \ell = 2 \)** - **Number of Electrons:** [_______] 3. **(c) \( n = 4 \)** - **Number of Electrons:** [_______] #### Explanation: - **Quantum Numbers**: - \( n \): Principal quantum number - \( \ell \): Azimuthal quantum number (angular momentum quantum number) - \( m_\ell \): Magnetic quantum number The Pauli exclusion principle states that no two electrons in an atom can have the same set of all four quantum numbers. Each electron must be unique in its quantum state. In the context above: - For part (a), the given quantum numbers \( n = 4, \ \ell = 3, \ m_\ell = -1 \) indicate a specific orbital within the atom. The spin quantum number (\( m_s \)) can either be \( +\frac{1}{2} \) or \( -\frac{1}{2} \). Thus, you can determine the number of electrons that can occupy this state. - For part (b), \( n = 3, \ \ell = 2 \) specifies a set of orbitals, and you must consider the possible values for \( m_\ell \) and \( m_s \) to find the total number of electrons. - For part (c), \( n = 4 \) indicates the principal quantum number, and you must assess the sublevels and orbital specifications within this level to find the maximum number of electrons it can accommodate.
### Application of the Pauli Exclusion Principle in Quantum States #### Hint: Make use of the hint button labeled "HINT" for further guidance on solving these problems. #### Problems: Apply the Pauli exclusion principle to determine the number of electrons that could occupy the quantum states described by the following: 1. **(a) \( n = 4, \ \ell = 3, \ m_\ell = -1 \)** - **Number of Electrons:** [_______] 2. **(b) \( n = 3, \ \ell = 2 \)** - **Number of Electrons:** [_______] 3. **(c) \( n = 4 \)** - **Number of Electrons:** [_______] #### Explanation: - **Quantum Numbers**: - \( n \): Principal quantum number - \( \ell \): Azimuthal quantum number (angular momentum quantum number) - \( m_\ell \): Magnetic quantum number The Pauli exclusion principle states that no two electrons in an atom can have the same set of all four quantum numbers. Each electron must be unique in its quantum state. In the context above: - For part (a), the given quantum numbers \( n = 4, \ \ell = 3, \ m_\ell = -1 \) indicate a specific orbital within the atom. The spin quantum number (\( m_s \)) can either be \( +\frac{1}{2} \) or \( -\frac{1}{2} \). Thus, you can determine the number of electrons that can occupy this state. - For part (b), \( n = 3, \ \ell = 2 \) specifies a set of orbitals, and you must consider the possible values for \( m_\ell \) and \( m_s \) to find the total number of electrons. - For part (c), \( n = 4 \) indicates the principal quantum number, and you must assess the sublevels and orbital specifications within this level to find the maximum number of electrons it can accommodate.
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11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Application of the Pauli Exclusion Principle in Quantum States
#### Hint:
Make use of the hint button labeled "HINT" for further guidance on solving these problems.
#### Problems:
Apply the Pauli exclusion principle to determine the number of electrons that could occupy the quantum states described by the following:
1. **(a) \( n = 4, \ \ell = 3, \ m_\ell = -1 \)**
- **Number of Electrons:** [_______]
2. **(b) \( n = 3, \ \ell = 2 \)**
- **Number of Electrons:** [_______]
3. **(c) \( n = 4 \)**
- **Number of Electrons:** [_______]
#### Explanation:
- **Quantum Numbers**:
- \( n \): Principal quantum number
- \( \ell \): Azimuthal quantum number (angular momentum quantum number)
- \( m_\ell \): Magnetic quantum number
The Pauli exclusion principle states that no two electrons in an atom can have the same set of all four quantum numbers. Each electron must be unique in its quantum state. In the context above:
- For part (a), the given quantum numbers \( n = 4, \ \ell = 3, \ m_\ell = -1 \) indicate a specific orbital within the atom. The spin quantum number (\( m_s \)) can either be \( +\frac{1}{2} \) or \( -\frac{1}{2} \). Thus, you can determine the number of electrons that can occupy this state.
- For part (b), \( n = 3, \ \ell = 2 \) specifies a set of orbitals, and you must consider the possible values for \( m_\ell \) and \( m_s \) to find the total number of electrons.
- For part (c), \( n = 4 \) indicates the principal quantum number, and you must assess the sublevels and orbital specifications within this level to find the maximum number of electrons it can accommodate.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F571545a5-7051-4737-8c51-eeaf309ab3a3%2Fb344a40a-4a71-4558-84d0-a881468a7378%2Fdo05mm_processed.png&w=3840&q=75)
Transcribed Image Text:### Application of the Pauli Exclusion Principle in Quantum States
#### Hint:
Make use of the hint button labeled "HINT" for further guidance on solving these problems.
#### Problems:
Apply the Pauli exclusion principle to determine the number of electrons that could occupy the quantum states described by the following:
1. **(a) \( n = 4, \ \ell = 3, \ m_\ell = -1 \)**
- **Number of Electrons:** [_______]
2. **(b) \( n = 3, \ \ell = 2 \)**
- **Number of Electrons:** [_______]
3. **(c) \( n = 4 \)**
- **Number of Electrons:** [_______]
#### Explanation:
- **Quantum Numbers**:
- \( n \): Principal quantum number
- \( \ell \): Azimuthal quantum number (angular momentum quantum number)
- \( m_\ell \): Magnetic quantum number
The Pauli exclusion principle states that no two electrons in an atom can have the same set of all four quantum numbers. Each electron must be unique in its quantum state. In the context above:
- For part (a), the given quantum numbers \( n = 4, \ \ell = 3, \ m_\ell = -1 \) indicate a specific orbital within the atom. The spin quantum number (\( m_s \)) can either be \( +\frac{1}{2} \) or \( -\frac{1}{2} \). Thus, you can determine the number of electrons that can occupy this state.
- For part (b), \( n = 3, \ \ell = 2 \) specifies a set of orbitals, and you must consider the possible values for \( m_\ell \) and \( m_s \) to find the total number of electrons.
- For part (c), \( n = 4 \) indicates the principal quantum number, and you must assess the sublevels and orbital specifications within this level to find the maximum number of electrons it can accommodate.
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