Understanding Quantum Numbers
Quantum numbers are pivotal in determining the properties of atomic orbitals. Each orbital is defined by a set of four quantum numbers: n, l, m, and s. Here, we focus primarily on n (principal quantum number) and l (azimuthal quantum number).
Principal Quantum Number (n)
- The principal quantum number (n) indicates the energy level of an electron in an atom.
- For n=4, this means we are looking at the fourth energy level.
Azimuthal Quantum Number (l)
- The azimuthal quantum number (l) defines the shape of the orbital and can take values from 0 to n-1.
- For l=3, this corresponds to the f-subshell, as the values of l represent:
- l=0: s
- l=1: p
- l=2: d
- l=3: f
Orbital Designation
- When given n=4 and l=3, we seek the orbital that corresponds to these quantum numbers.
- The only orbital that meets these criteria is 4f, as it indicates the fourth energy level with an f-subshell.
Evaluating the Options
- Option a) 4f: Correct, as it corresponds to n=4 and l=3.
- Option b) 4d: Incorrect, because l=2, not l=3.
- Option c) 3d: Incorrect, since n=3, not n=4.
- Option d) 4p: Incorrect, as l=1, not l=3.
Conclusion
The correct choice is option 'A' (4f) because it accurately represents the quantum numbers n=4 and l=3. Understanding these fundamental principles is essential for grasping the structure of atoms and the behavior of electrons within them.