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List all the possible quantum numbers (n,l,me) for the n = 5 level in atomic hydrogen.

List all the possible quantum numbers (n,l,me) for the n = 5 level in atomic hydrogen.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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### Quantum Numbers for \( n = 5 \) in Atomic Hydrogen **Question:** List all the possible quantum numbers (\( n, \ell, m_{\ell} \)) for the \( n = 5 \) level in atomic hydrogen. **Answer:** In atomic hydrogen, the quantum numbers can be described as follows: 1. **Principal Quantum Number (\( n \))**: Specifies the energy level of the electron. For this question, \( n = 5 \). 2. **Angular Momentum Quantum Number (\( \ell \))**: Specifies the shape of the orbital, where \( \ell \) can range from \( 0 \) to \( n-1 \). Thus, for \( n = 5 \), \( \ell \) can be \( 0, 1, 2, 3, \) or \( 4 \). 3. **Magnetic Quantum Number (\( m_{\ell} \))**: Specifies the orientation of the orbital, where \( m_{\ell} \) can range from \( -\ell \) to \( +\ell \). Here are all the possible quantum numbers for \( n = 5 \): - For \( \ell = 0 \): - \( m_{\ell} = 0 \) - For \( \ell = 1 \): - \( m_{\ell} = -1, 0, +1 \) - For \( \ell = 2 \): - \( m_{\ell} = -2, -1, 0, +1, +2 \) - For \( \ell = 3 \): - \( m_{\ell} = -3, -2, -1, 0, +1, +2, +3 \) - For \( \ell = 4 \): - \( m_{\ell} = -4, -3, -2, -1, 0, +1, +2, +3, +4 \) ### Summary of Possible Quantum Numbers - \( n = 5 \) - \( \ell = 0, 1, 2, 3, 4 \) - \( m_{\ell} \) values corresponding to each \( \ell \): - \( \ell = 0 \): \( m_{\ell} = 0 \) - \( \ell = 1 \): \( m
Transcribed Image Text:### Quantum Numbers for \( n = 5 \) in Atomic Hydrogen **Question:** List all the possible quantum numbers (\( n, \ell, m_{\ell} \)) for the \( n = 5 \) level in atomic hydrogen. **Answer:** In atomic hydrogen, the quantum numbers can be described as follows: 1. **Principal Quantum Number (\( n \))**: Specifies the energy level of the electron. For this question, \( n = 5 \). 2. **Angular Momentum Quantum Number (\( \ell \))**: Specifies the shape of the orbital, where \( \ell \) can range from \( 0 \) to \( n-1 \). Thus, for \( n = 5 \), \( \ell \) can be \( 0, 1, 2, 3, \) or \( 4 \). 3. **Magnetic Quantum Number (\( m_{\ell} \))**: Specifies the orientation of the orbital, where \( m_{\ell} \) can range from \( -\ell \) to \( +\ell \). Here are all the possible quantum numbers for \( n = 5 \): - For \( \ell = 0 \): - \( m_{\ell} = 0 \) - For \( \ell = 1 \): - \( m_{\ell} = -1, 0, +1 \) - For \( \ell = 2 \): - \( m_{\ell} = -2, -1, 0, +1, +2 \) - For \( \ell = 3 \): - \( m_{\ell} = -3, -2, -1, 0, +1, +2, +3 \) - For \( \ell = 4 \): - \( m_{\ell} = -4, -3, -2, -1, 0, +1, +2, +3, +4 \) ### Summary of Possible Quantum Numbers - \( n = 5 \) - \( \ell = 0, 1, 2, 3, 4 \) - \( m_{\ell} \) values corresponding to each \( \ell \): - \( \ell = 0 \): \( m_{\ell} = 0 \) - \( \ell = 1 \): \( m
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