Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Transcribed Image Text:### Quantum Numbers Exercise
**Problem Statement:**
Circle the set or sets of quantum numbers that are erroneous.
**Options:**
a) \( n = 4, \, l = 2, \, m_l = -2 \)
b) \( n = 2, \, l = 2, \, m_l = +1, \, m_s = -\frac{1}{2} \)
c) \( n = 5, \, l = 3, \, m_l = -3 \)
d) \( n = 1, \, l = 1 \)
**Analysis:**
The problem asks to identify incorrect sets of quantum numbers among the given options. Each set is defined by quantum numbers including:
- Principal quantum number (\( n \))
- Azimuthal quantum number (\( l \))
- Magnetic quantum number (\( m_l \))
- Spin quantum number (\( m_s \)) (only given in option b)
**Explanation:**
- **Principal Quantum Number (\( n \))**: Indicates the energy level and size of the orbital, which must be a positive integer.
- **Azimuthal Quantum Number (\( l \))**: Ranges from 0 to \( n-1 \). It defines the shape of the orbital.
- **Magnetic Quantum Number (\( m_l \))**: Ranges from \(-l\) to \(+l\). It specifies the orientation of the orbital in space.
- **Spin Quantum Number (\( m_s \))**: Can be either \(-\frac{1}{2}\) or \(+\frac{1}{2}\). It represents the two possible spin states of an electron.
**Identifying Errors:**
- **(a)** All quantum numbers are valid, as \( l \) and \( m_l \) are within the correct range for \( n = 4 \).
- **(b)** Incorrect, because \( l \) cannot equal \( n \). For \( n = 2 \), \( l \) can only be 0 or 1.
- **(c)** All quantum numbers are valid. Both \( l \) and \( m_l \) are correctly within range for \( n = 5 \).
- **(d)** Incorrect, because \( l \) cannot be equal to or greater than \( n \). For \( n = 1 \),
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