(b) Identify the number of nodes; that is, identify places where the electron density is zero, in the 2px orbital; in the 3s orbital.

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Understand that nodes are regions in an atomic orbital where the probability of finding an electron is zero.

For the 2px orbital, recognize that it is a p orbital, which has one nodal plane passing through the nucleus.

Visualize the 2px orbital as having a nodal plane perpendicular to the x-axis, where the electron density is zero.

For the 3s orbital, note that s orbitals are spherical and have radial nodes.

Determine the number of radial nodes in the 3s orbital using the formula: number of radial nodes = n - l - 1, where n is the principal quantum number and l is the azimuthal quantum number.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Atomic Orbitals

Atomic orbitals are regions in an atom where there is a high probability of finding electrons. Each orbital is characterized by its shape and energy level, with common types including s, p, d, and f orbitals. The 2px and 3s orbitals differ in their energy levels and shapes, influencing their electron density distributions.

Nodes in Orbitals

Nodes are specific points or regions in an orbital where the probability of finding an electron is zero. In atomic orbitals, nodes can be classified as radial nodes (spherical surfaces) or angular nodes (planes or angles). The number of nodes increases with the principal quantum number, affecting the shape and energy of the orbital.

Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and the electrons in them. The principal quantum number (n) indicates the energy level, while the angular momentum quantum number (l) defines the shape of the orbital. For example, the 2px orbital has n=2 and l=1, while the 3s orbital has n=3 and l=0, which helps determine their respective node structures.

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Principal Quantum Number

Related Practice

Textbook Question

(d) For the hydrogen atom, list the following orbitals in order of increasing energy (that is, most stable ones first): 4f, 6s, 3d, 1s, 2p.

Textbook Question

(a) For an He+ ion, do the 2s and 2p orbitals have the same energy? If not, which orbital has a lower energy?

Textbook Question

(c) What can you say about the average distance from the nucleus of an electron in a 2s orbital as compared with a 3s orbital?

Textbook Question

(b) If we add one electron to form the He atom, would your answer to part (a) change?

Textbook Question

(a) With reference to Figure 6.19, what is the relationship between the number of nodes in an s orbital and the value of the principal quantum number?

Textbook Question

(d) For the hydrogen atom, list the following orbitals in order of increasing energy: 3s, 2s, 2p, 5s, 4d.