To determine the second quantum number (also known as the azimuthal quantum number, typically denoted by [tex]\( l \)[/tex]) for the [tex]\( 3p^1 \)[/tex] electron in an aluminum atom with the electronic configuration [tex]\( 1s^2 2s^2 2p^6 3s^2 3p^1 \)[/tex], we need to follow a systematic approach.
1. Identify the Principal Quantum Number (n):
- The given electron is in the [tex]\( 3p^1 \)[/tex] orbital.
- The principal quantum number, [tex]\( n \)[/tex], for this electron is 3 since it is in the third energy level.
2. Understand the Azimuthal Quantum Number (l):
- The second quantum number, [tex]\( l \)[/tex], defines the orbital shape and is dependent on the principal quantum number [tex]\( n \)[/tex].
- For any given principal quantum number [tex]\( n \)[/tex], [tex]\( l \)[/tex] can take integer values from 0 to [tex]\( n-1 \)[/tex].
3. Assigning Values Based on Orbital Type:
- [tex]\( l = 0 \)[/tex] corresponds to the [tex]\( s \)[/tex]-orbitals.
- [tex]\( l = 1 \)[/tex] corresponds to the [tex]\( p \)[/tex]-orbitals.
- [tex]\( l = 2 \)[/tex] corresponds to the [tex]\( d \)[/tex]-orbitals.
- [tex]\( l = 3 \)[/tex] corresponds to the [tex]\( f \)[/tex]-orbitals.
4. Determine [tex]\( l \)[/tex] for the Given Orbital:
- The given electron is in a [tex]\( p \)[/tex]-orbital.
- For a [tex]\( p \)[/tex]-orbital, the azimuthal quantum number [tex]\( l \)[/tex] is 1.
Thus, the second quantum number [tex]\( l \)[/tex] for the [tex]\( 3p^1 \)[/tex] electron in aluminum is [tex]\( 1 \)[/tex].
Therefore, the correct answer is:
C. [tex]\( I = 1 \)[/tex]
