The accompanying drawing shows a contour plot for a dyz orbital. Consider the quantum numbers that could potentially correspond to this orbital. (c) What is the largest possible value of the magnetic quantum number, ml?

Verified step by step guidance

1. Identify the type of orbital shown in the contour plot. The dyz orbital is a type of d orbital.
2. Recall that d orbitals correspond to the azimuthal quantum number, l, which is equal to 2.
3. Understand that the magnetic quantum number, ml, can take on integer values ranging from -l to +l.
4. For a d orbital (l = 2), the possible values of ml are -2, -1, 0, +1, and +2.
5. Determine the largest possible value of the magnetic quantum number, ml, which is +2.

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 of the orbital, orientation, and spin, respectively.

Magnetic Quantum Number (ml)

The magnetic quantum number (ml) determines the orientation of an orbital in space relative to the three axes (x, y, z). For a given azimuthal quantum number (l), ml can take on integer values ranging from -l to +l, including zero. For example, for a d orbital (where l = 2), ml can be -2, -1, 0, +1, or +2, indicating the different orientations of the d orbitals.

dyz Orbital

The dyz orbital is one of the five d orbitals and is characterized by its specific shape and orientation in three-dimensional space. It is oriented in the yz-plane and has a distinct lobular structure, which is evident in the contour plot. Understanding the shape and orientation of the dyz orbital is crucial for determining its corresponding quantum numbers, particularly the magnetic quantum number (ml).