(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?

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The 2s and 3s orbitals are both spherical in shape, but they differ in size and energy level.

The principal quantum number (n) indicates the energy level and size of the orbital. For 2s, n=2, and for 3s, n=3.

As the principal quantum number increases, the average distance of the electron from the nucleus also increases.

Therefore, electrons in a 3s orbital are, on average, further from the nucleus than electrons in a 2s orbital.

This is because the 3s orbital is larger and has a higher energy level than the 2s orbital.

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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 around the nucleus of an atom where electrons are likely to be found. Each orbital is defined by a set of quantum numbers, which describe its shape, size, and orientation. The 's' orbitals are spherical in shape, with the 2s and 3s orbitals representing different energy levels, where the principal quantum number (n) indicates the energy level and size of the orbital.

Principal Quantum Number (n)

The principal quantum number (n) is a key quantum number that determines the energy level and size of an electron's orbital. As n increases, the average distance of the electron from the nucleus also increases, leading to larger orbitals. For example, a 3s orbital has a higher principal quantum number than a 2s orbital, indicating that electrons in the 3s orbital are, on average, found further from the nucleus than those in the 2s orbital.

Electron Density and Probability Distribution

Electron density refers to the likelihood of finding an electron in a particular region around the nucleus. The probability distribution of an electron in an orbital can be visualized using electron density maps. In the case of 2s and 3s orbitals, the 3s orbital has a larger volume and a greater average distance from the nucleus, reflecting a higher probability of finding the electron farther away compared to the 2s orbital.

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Textbook Question

Sketch the shape and orientation of the following types of orbitals: (a) s, (b) p_z, (c) d_xy.

Textbook Question

Sketch the shape and orientation of the following types of orbitals: (a) p_x, (b) d_z2, (c) d_{x2 - y2}.

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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) 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

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