How many electrons can be described by the quantum numbers n=2, l=2, m=0. O 1 O 3 O 6 2.

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**Title: Quantum Numbers and Electron Configuration**

**Question:**
How many electrons can be described by the quantum numbers \( n=2, l=2, m_l=0 \)?

**Options:**
- 1
- 3
- 6
- 0
- 2

**Explanation:**
To determine how many electrons can be described by the given quantum numbers \( n=2, l=2, m_l=0 \), we need to understand the meaning and restrictions of each quantum number:

1. **Principal Quantum Number (\(n\))**: Indicates the main energy level. \( n = 2 \) refers to the second energy level.
2. **Azimuthal Quantum Number (\(l\))**: Represents the subshell (or angular momentum). \( l = 2 \) corresponds to the \(d\)-subshell.
3. **Magnetic Quantum Number (\(m_l\))**: Specifies the orientation of the orbital. \( m_l = 0 \) means the orbital is oriented in a specific way in the magnetic field.

For given \( n \) and \( l \):
- \( n = 2 \)
- \( l = 2 \) (which is typically associated with the third principal quantum number. It seems there is probably a misunderstanding. The maximum \( l \) value for \( n=2 \) should be \( l=1 \), which corresponds to the \( p \)-subshell. However, assuming the context is set for advanced cases: assuming \( n=2 \), and considering \( l=2 \), then \( n \) should at least be 3 for \( l=2 \)).

Given \( m_l = 0 \), each orientation (each \( m_l \) value) can hold one electron with each of the two possible spin states (\( m_s = +\frac{1}{2} \) and \( m_s = -\frac{1}{2} \)).

Therefore, the answer is **2 electrons**: one for each possible spin state in the orbital described by \( n=2, l=2, m_l=0 \).

**Correct Answer:**
- 2
Transcribed Image Text:**Title: Quantum Numbers and Electron Configuration** **Question:** How many electrons can be described by the quantum numbers \( n=2, l=2, m_l=0 \)? **Options:** - 1 - 3 - 6 - 0 - 2 **Explanation:** To determine how many electrons can be described by the given quantum numbers \( n=2, l=2, m_l=0 \), we need to understand the meaning and restrictions of each quantum number: 1. **Principal Quantum Number (\(n\))**: Indicates the main energy level. \( n = 2 \) refers to the second energy level. 2. **Azimuthal Quantum Number (\(l\))**: Represents the subshell (or angular momentum). \( l = 2 \) corresponds to the \(d\)-subshell. 3. **Magnetic Quantum Number (\(m_l\))**: Specifies the orientation of the orbital. \( m_l = 0 \) means the orbital is oriented in a specific way in the magnetic field. For given \( n \) and \( l \): - \( n = 2 \) - \( l = 2 \) (which is typically associated with the third principal quantum number. It seems there is probably a misunderstanding. The maximum \( l \) value for \( n=2 \) should be \( l=1 \), which corresponds to the \( p \)-subshell. However, assuming the context is set for advanced cases: assuming \( n=2 \), and considering \( l=2 \), then \( n \) should at least be 3 for \( l=2 \)). Given \( m_l = 0 \), each orientation (each \( m_l \) value) can hold one electron with each of the two possible spin states (\( m_s = +\frac{1}{2} \) and \( m_s = -\frac{1}{2} \)). Therefore, the answer is **2 electrons**: one for each possible spin state in the orbital described by \( n=2, l=2, m_l=0 \). **Correct Answer:** - 2
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