Give the numerical values of n and l corresponding to each of the following orbital designations: (a) 3p (b) 2s (c) 4f

Verified step by step guidance

1. Understand that the principal quantum number \( n \) indicates the energy level or shell of the electron. For the given orbital designation '3p', the number '3' represents the principal quantum number \( n \).
2. Recognize that the azimuthal quantum number \( l \) determines the shape of the orbital. The letter 'p' corresponds to \( l = 1 \).
3. Combine the information: for the '3p' orbital, \( n = 3 \) and \( l = 1 \).
4. Recall that the azimuthal quantum number \( l \) can take values from 0 to \( n-1 \). For \( n = 3 \), \( l \) can be 0, 1, or 2, which correspond to 's', 'p', and 'd' orbitals respectively.
5. Verify that the given designation '3p' correctly matches \( n = 3 \) and \( l = 1 \), confirming the orbital's energy level and shape.

Key Concepts

Quantum Numbers

Quantum numbers are a set of numerical values that describe the unique quantum state of an electron in an atom. The principal quantum number (n) indicates the energy level and size of the orbital, while the azimuthal quantum number (l) defines the shape of the orbital. Together, these numbers help in identifying the location and energy of electrons.

Principal Quantum Number (n)

The principal quantum number (n) is a positive integer that represents the main energy level of an electron in an atom. It can take values of 1, 2, 3, and so on, with higher values corresponding to higher energy levels and larger orbitals. For the 3p orbital, n is 3, indicating it is in the third energy level.

Azimuthal Quantum Number (l)

The azimuthal quantum number (l) determines the shape of the orbital and can take integer values from 0 to (n-1). Each value of l corresponds to a specific type of orbital: 0 for s, 1 for p, 2 for d, and 3 for f. For the 3p orbital, l is 1, indicating it has a p-shaped configuration.