What are the possible values of m_l for each value of l? a. 0

Key Concepts

Quantum Numbers

Quantum numbers are a set of numerical values that describe the unique quantum state of an electron in an atom. They include the principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (ml), and spin quantum number (ms). Each quantum number provides specific information about the electron's energy level, shape, orientation, and spin.

Azimuthal Quantum Number (l)

The azimuthal quantum number (l) determines the shape of an electron's orbital and can take on integer values from 0 to n-1, where n is the principal quantum number. For example, if n=2, l can be 0 or 1, corresponding to s and p orbitals, respectively. The value of l is crucial for understanding the types of orbitals and their geometrical arrangements.

Magnetic Quantum Number (ml)

The magnetic quantum number (ml) specifies the orientation of an orbital in space and can take on integer values ranging from -l to +l, including zero. For each value of l, there are 2l + 1 possible values of ml. For instance, if l=1 (p orbital), ml can be -1, 0, or +1, indicating the three different orientations of p orbitals.