To determine the possible values of the magnetic quantum number [tex]\( m_l \)[/tex] for an electron in a [tex]\( 2p \)[/tex] orbital, let's break it down step-by-step.
1. Principle Quantum Number (n): For a [tex]\( 2p \)[/tex] orbital, the principal quantum number is [tex]\( n = 2 \)[/tex].
2. Azimuthal Quantum Number (l): The azimuthal quantum number, [tex]\( l \)[/tex], defines the shape of the orbital and for a [tex]\( p \)[/tex]-orbital, [tex]\( l = 1 \)[/tex].
3. Magnetic Quantum Number (m_l): The magnetic quantum number depends on the azimuthal quantum number [tex]\( l \)[/tex]. It can take on integer values ranging from [tex]\( -l \)[/tex] to [tex]\( +l \)[/tex].
- For [tex]\( l = 1 \)[/tex]:
[tex]\[
m_l \in \{-1, 0, +1\}
\][/tex]
The given question asks for a possible value of [tex]\( m_l \)[/tex] for a [tex]\( 2p \)[/tex] electron in phosphorus. We know that [tex]\( m_l \)[/tex] can only be [tex]\(-1\)[/tex], [tex]\(0\)[/tex], or [tex]\(+1\)[/tex] for [tex]\( l = 1 \)[/tex].
Next, let’s review the given answer choices:
- A. [tex]\( m_l = -2 \)[/tex]
- B. [tex]\( m_l = 2 \)[/tex]
- C. [tex]\( m_l = 3 \)[/tex]
- D. [tex]\( m_l = -1 \)[/tex]
Among these options, only [tex]\( m_l = -1 \)[/tex] falls within the permissible range of [tex]\(-1, 0, +1\)[/tex].
Therefore, the correct answer is:
D. [tex]\( m_l = -1 \)[/tex]
