Be sure to answer all parts. An electron in an atom is in the n 3 and =1 quantum level. (a) Select the possible values of m, that it can have. m, = 0, 1 m =-1, 0, 1 m=0, 1, 2, 3 m =-2,-1, 0, 1, 2 (b) What are all of the possible values of at n=3? e=0, 1, 2 e=-3,-2,-1, 0, 1, 2, 3 2=-2,-1, 0, 1, 2 e = 0, 1, 2, 3

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**Quantum Mechanics: Analyzing Quantum Levels**

**Be sure to answer all parts.**

**An electron in an atom is in the \( n = 3 \) and \( \ell = 1 \) quantum level.**

**(a) Select the possible values of \( m_{\ell} \) that it can have.**
- \( \circ \quad m_{\ell} = 0, 1 \)
- \( \circ \quad m_{\ell} = -1, 0, 1 \)
- \( \circ \quad m_{\ell} = 0, 1, 2, 3 \)
- \( \circ \quad m_{\ell} = -2, -1, 0, 1, 2 \)

**(b) What are all of the possible values of \( \ell \) at \( n = 3 \)?**
- \( \circ \quad \ell = 0, 1, 2 \)
- \( \circ \quad \ell = -3, -2, -1, 0, 1, 2, 3 \)
- \( \circ \quad \ell = -2, -1, 0, 1, 2 \)
- \( \circ \quad \ell = 0, 1, 2, 3 \)

**Explanation of Concepts:**

Quantum numbers are fundamental to understanding the quantum mechanical model of the atom. They describe values of conserved quantities in the dynamics of the quantum system.

1. **Principal Quantum Number (\( n \))**: Determines the energy level in which the electron resides. In this context, \( n = 3 \).

2. **Azimuthal Quantum Number (\( \ell \))**: Defines the subshell and determines the shape of the orbital. Here, \( \ell = 1 \).

3. **Magnetic Quantum Number (\( m_{\ell} \))**: Describes the orientation of the orbital in space relative to the other orbitals. It can take on integer values between \( -\ell \) and \( +\ell \).

In this problem:

- For \( n = 3 \) and \( \ell = 1 \), the possible values of \( m_{\ell} \) are -1, 0, and 1. 
- When considering all possible values of \( \ell \) for
Transcribed Image Text:**Quantum Mechanics: Analyzing Quantum Levels** **Be sure to answer all parts.** **An electron in an atom is in the \( n = 3 \) and \( \ell = 1 \) quantum level.** **(a) Select the possible values of \( m_{\ell} \) that it can have.** - \( \circ \quad m_{\ell} = 0, 1 \) - \( \circ \quad m_{\ell} = -1, 0, 1 \) - \( \circ \quad m_{\ell} = 0, 1, 2, 3 \) - \( \circ \quad m_{\ell} = -2, -1, 0, 1, 2 \) **(b) What are all of the possible values of \( \ell \) at \( n = 3 \)?** - \( \circ \quad \ell = 0, 1, 2 \) - \( \circ \quad \ell = -3, -2, -1, 0, 1, 2, 3 \) - \( \circ \quad \ell = -2, -1, 0, 1, 2 \) - \( \circ \quad \ell = 0, 1, 2, 3 \) **Explanation of Concepts:** Quantum numbers are fundamental to understanding the quantum mechanical model of the atom. They describe values of conserved quantities in the dynamics of the quantum system. 1. **Principal Quantum Number (\( n \))**: Determines the energy level in which the electron resides. In this context, \( n = 3 \). 2. **Azimuthal Quantum Number (\( \ell \))**: Defines the subshell and determines the shape of the orbital. Here, \( \ell = 1 \). 3. **Magnetic Quantum Number (\( m_{\ell} \))**: Describes the orientation of the orbital in space relative to the other orbitals. It can take on integer values between \( -\ell \) and \( +\ell \). In this problem: - For \( n = 3 \) and \( \ell = 1 \), the possible values of \( m_{\ell} \) are -1, 0, and 1. - When considering all possible values of \( \ell \) for
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