Ch.6 - Electronic Structure of Atoms

Brown - Chemistry: The Central Science 15th Edition

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Brown 15th Edition

Ch.6 - Electronic Structure of Atoms

Problem 59a

Chapter 6, Problem 59a

A certain orbital of the hydrogen atom has n = 4 and l = 2. a. What are the possible values of ml for this orbital?

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Identify the given quantum numbers: n = 4 and l = 2.

Understand that the magnetic quantum number, m_l, depends on the azimuthal quantum number, l.

Recall that the possible values of m_l range from -l to +l, including zero.

For l = 2, list the possible values of m_l: -2, -1, 0, 1, 2.

Conclude that the possible values of m_l for this orbital are -2, -1, 0, 1, and 2.

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Key Concepts

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

Quantum Numbers

Quantum numbers are a set of numerical values that describe the unique quantum state of an electron in an atom. The four quantum numbers are principal (n), azimuthal (l), magnetic (ml), and spin (ms). Each number provides specific information about the electron's energy level, shape, orientation, and spin, which are essential for understanding electron configurations.

Principal Quantum Number (n)

The principal quantum number (n) indicates the main energy level or shell of an electron in an atom. It can take positive integer values (1, 2, 3, ...), with higher values corresponding to electrons that are further from the nucleus and have higher energy. In this case, n = 4 signifies that the electron is in the fourth energy level.

Magnetic Quantum Number (ml)

The magnetic quantum number (ml) describes the orientation of an orbital in space and can take on integer values ranging from -l to +l, where l is the azimuthal quantum number. For l = 2, which corresponds to a d-orbital, ml can have values of -2, -1, 0, +1, and +2, indicating the different orientations of the d-orbitals.

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Related Practice

Textbook Question

How many unique combinations of the quantum numbers l and 𝑚𝑙 are there when b. n = 4?

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Textbook Question

(a) For n = 4, what are the possible values of l?

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Textbook Question

Which of the following represent impossible combinations of n and l? (a) 1p (b) 4s (c) 5f (d) 2d

1080

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Textbook Question

Give the values for n, l, and 𝑚𝑙 for a. each orbital in the 2p subshell

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Textbook Question

For the table that follows, write which orbital goes with the quantum numbers. Don't worry about x, y, z subscripts. If the quantum numbers are not allowed, write 'not allowed.' n l ml Orbital 2 1 -1 2p (example) 1 0 0 3 -3 2 3 2 -2 2 0 -1 0 0 0 4 2 1 5 3 0

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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.

1177

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