The accompanying drawing shows a contour plot for a dyz orbital. Consider the quantum numbers that could potentially correspond to this orbital. (d) The probability density goes to zero along which of the following planes: xy, xz, or yz?

Key Concepts

Quantum Numbers

Quantum numbers are sets 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 (m_l), and spin quantum number (m_s). For a dyz orbital, the relevant quantum numbers are n, l=2 (for d orbitals), and m_l= -1 or +1, indicating the orientation of the orbital.

Orbital Shapes and Probability Density

Orbitals are regions in an atom where there is a high probability of finding electrons. The shape of an orbital, such as the dyz orbital, is determined by its angular momentum quantum number (l). The contour plot illustrates the lobes of the dyz orbital, which are oriented along the y and z axes, indicating where the probability density is high, while the density is zero along the xz plane.

Nodes in Orbitals

Nodes are regions in an orbital where the probability density of finding an electron is zero. For the dyz orbital, there is a nodal plane along the xz plane, meaning that at this plane, the probability of finding an electron is zero. Understanding the concept of nodes is crucial for visualizing the spatial distribution of electrons in different orbitals.