What are the possible values of m_l for each value of l? c. 2 d. 3

Verified step by step guidance

1. Identify the quantum number 'l' given in the problem. Here, 'l' is equal to 2.
2. Recall that the magnetic quantum number 'ml' can take on integer values ranging from -l to +l, including zero.
3. List all the possible integer values starting from -l to +l for l = 2. This means starting from -2 to +2.
4. The possible values of 'ml' when 'l' equals 2 are -2, -1, 0, 1, and 2.
5. These values represent the orientation of the orbital angular momentum in space relative to an external magnetic field.

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 l = 2, it corresponds to a d orbital. The value of l influences the angular momentum of the electron and the type of subshell it occupies.

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 a given value of l, the number of possible ml values is 2l + 1. For instance, if l = 2, the possible values of ml are -2, -1, 0, +1, and +2, indicating five different orientations for the d orbitals.