To determine the fourth quantum number for one of the electrons in the [tex]\( 4p \)[/tex] energy sublevel of bromine, we need to understand the different types of quantum numbers in quantum mechanics.
There are four quantum numbers that describe the properties of an electron in an atom:
1. Principal Quantum Number (n): This quantum number indicates the energy level of the electron. For the [tex]\( 4p \)[/tex] sublevel, [tex]\( n = 4 \)[/tex].
2. Angular Momentum Quantum Number (l): This quantum number describes the shape of the orbital. For a [tex]\( p \)[/tex] orbital, [tex]\( l = 1 \)[/tex].
3. Magnetic Quantum Number (m_l): This quantum number indicates the orientation of the orbital in space. For [tex]\( p \)[/tex] orbitals, [tex]\( m_l \)[/tex] can take any integer value from [tex]\( -l \)[/tex] to [tex]\( l \)[/tex], i.e., [tex]\( m_l = -1, 0, \text{or} \, 1 \)[/tex].
4. Spin Quantum Number (m_s): This quantum number indicates the spin of the electron and can take one of two values: [tex]\( -\frac{1}{2} \)[/tex] or [tex]\( \frac{1}{2} \)[/tex].
Given that we are tasked with finding the fourth quantum number, which is the spin quantum number (m_s), we need to consider the allowed values for [tex]\( m_s \)[/tex]. The spin quantum number can only be:
- [tex]\( m_s = -\frac{1}{2} \)[/tex]
- [tex]\( m_s = \frac{1}{2} \)[/tex]
Looking at the options provided:
A. [tex]\( m_s = -\frac{1}{2} \)[/tex]
B. [tex]\( m_s = 4 \)[/tex]
C. [tex]\( m_s = 1 \)[/tex]
D. [tex]\( m_s = 0 \)[/tex]
We recognize that the only valid values for [tex]\( m_s \)[/tex] are [tex]\( -\frac{1}{2} \)[/tex] and [tex]\( \frac{1}{2} \)[/tex]. Among the provided options, the only valid value is:
[tex]\[ A. \, m_s = -\frac{1}{2} \][/tex]
[tex]\[
\boxed{A}
\][/tex]
