Certainly! Let's analyze each set of quantum numbers and determine the type of orbital corresponding to the given values of [tex]\( n \)[/tex] and [tex]\( l \)[/tex].
### Quantum Numbers and Orbital Types
Quantum numbers determine the properties of orbitals:
1. [tex]\( n \)[/tex] (principal quantum number): Specifies the energy level and relative size of the orbital.
2. [tex]\( l \)[/tex] (azimuthal quantum number): Specifies the shape of the orbital. The value of [tex]\( l \)[/tex] ranges from 0 to [tex]\( n-1 \)[/tex] and is associated with specific types of orbitals:
- [tex]\( l = 0 \)[/tex]: s-orbital
- [tex]\( l = 1 \)[/tex]: p-orbital
- [tex]\( l = 2 \)[/tex]: d-orbital
- [tex]\( l = 3 \)[/tex]: f-orbital
Let's determine the type of orbital for each given set of quantum numbers.
### Set p: [tex]\( n = 2 \)[/tex], [tex]\( l = 0 \)[/tex]
- [tex]\( n \)[/tex] (principal quantum number) = 2, so it's the second energy level.
- [tex]\( l \)[/tex] (azimuthal quantum number) = 0, which corresponds to an s-orbital.
Thus, the type of orbital for this set is:
s-orbital
### Set q: [tex]\( n = 3 \)[/tex], [tex]\( l = 2 \)[/tex]
- [tex]\( n \)[/tex] (principal quantum number) = 3, so it's the third energy level.
- [tex]\( l \)[/tex] (azimuthal quantum number) = 2, which corresponds to a d-orbital.
Thus, the type of orbital for this set is:
d-orbital
### Set r: [tex]\( n = 5 \)[/tex], [tex]\( l = 1 \)[/tex]
- [tex]\( n \)[/tex] (principal quantum number) = 5, so it's the fifth energy level.
- [tex]\( l \)[/tex] (azimuthal quantum number) = 1, which corresponds to a p-orbital.
Thus, the type of orbital for this set is:
p-orbital
### Summary
For each set of quantum numbers, we have identified the following types of orbitals:
- Set [tex]\( p \)[/tex]: s-orbital
- Set [tex]\( q \)[/tex]: d-orbital
- Set [tex]\( r \)[/tex]: p-orbital
Therefore, the identified types of orbitals are:
- [tex]\( p \)[/tex]: s-orbital
- [tex]\( q \)[/tex]: d-orbital
- [tex]\( r \)[/tex]: p-orbital
