To determine the fourth quantum number, [tex]\( m_s \)[/tex], for a [tex]\( 3p^3 \)[/tex] electron, let's break down the steps involved:
### Step 1: Understanding Quantum Numbers
Every electron in an atom is described by a set of four quantum numbers:
1. Principal Quantum Number (n): Indicates the main energy level. For [tex]\( 3p^3 \)[/tex], [tex]\( n = 3 \)[/tex].
2. Azimuthal Quantum Number (l): Indicates the shape of the orbital. For [tex]\( p \)[/tex]-orbitals, [tex]\( l = 1 \)[/tex].
3. Magnetic Quantum Number (m_l): Indicates the orientation of the orbital. For [tex]\( p \)[/tex]-orbitals, [tex]\( m_l \)[/tex] can be [tex]\( -1, 0, \)[/tex] or [tex]\( +1 \)[/tex].
4. Spin Quantum Number (m_s): Indicates the spin of the electron. The spin quantum number, [tex]\( m_s \)[/tex], can only have values of [tex]\( +\frac{1}{2} \)[/tex] or [tex]\( -\frac{1}{2} \)[/tex].
### Step 2: Identifying the Fourth Quantum Number for [tex]\( 3p^3 \)[/tex]
For the [tex]\( 3p^3 \)[/tex] electron configuration, there are 3 electrons in the [tex]\( p \)[/tex]-orbital. Each electron can have one of the possible [tex]\( m_s \)[/tex] values, which are [tex]\( +\frac{1}{2} \)[/tex] or [tex]\( -\frac{1}{2} \)[/tex].
### Step 3: Determining the Given Options
Given the multiple choice options for [tex]\( m_s \)[/tex]:
- A. [tex]\( m_s = -1 \)[/tex]
- B. [tex]\( m_s = -\frac{1}{2} \)[/tex]
- C. [tex]\( m_s = +1 \)[/tex]
- D. [tex]\( m_s = 0 \)[/tex]
Among these options, the correct possible value for the spin quantum number [tex]\( m_s \)[/tex] is [tex]\( -\frac{1}{2} \)[/tex].
### Conclusion
The fourth quantum number for a [tex]\( 3p^3 \)[/tex] electron is [tex]\( m_s = -\frac{1}{2} \)[/tex]. This corresponds to option B.
