How many nodal surfaces does a 4s orbital have? Draw a cutaway representation of a 4s orbital showing the nodes and the regions of maximum electron probability.

Verified step by step guidance

1. Identify the principal quantum number (n) for the 4s orbital, which is 4.
2. Recall that the number of nodal surfaces in an s orbital is given by the formula: n - 1.
3. Calculate the number of nodal surfaces for the 4s orbital using the formula: 4 - 1.
4. Understand that a nodal surface is a region where the probability of finding an electron is zero.
5. Draw a cutaway representation of the 4s orbital, showing three nodal surfaces and regions of maximum electron probability between these nodal surfaces.

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. For a 4s orbital, n=4 and l=0, indicating a spherical shape.

Nodal Surfaces

Nodal surfaces are regions in an atomic orbital where the probability of finding an electron is zero. The number of nodal surfaces in an orbital is determined by the azimuthal quantum number (l). For a 4s orbital, which has l=0, there is one radial node, meaning it has one nodal surface separating regions of different electron density.

Electron Probability Density

Electron probability density refers to the likelihood of finding an electron in a particular region of space around the nucleus. This concept is visualized through electron density plots, where darker areas indicate higher probabilities. In the case of the 4s orbital, the representation shows regions of maximum electron probability and the spherical shape of the orbital.