6) Circle the set or sets offquontum.nucmbers: thatis orare erroneous. a)n=4l=2 me=-2 (6)h=22=2 me=+1 ms=-1/2 C)n=S l=3. d)n=1 l=1 me =-3

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### 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 \( n = 1 \),
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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