Ch.6 - Electronic Structure of Atoms

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th 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 = 3. (a) What are the possible values of ml for this orbital?

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Identify the given quantum numbers: n = 4 and l = 3.

Recall that the magnetic quantum number, m_l, can have integer values ranging from -l to +l.

For l = 3, determine the range of m_l values: m_l can be -3, -2, -1, 0, 1, 2, or 3.

List all possible m_l values for l = 3: m_l = -3, -2, -1, 0, 1, 2, 3.

Conclude that these are the possible values of m_l for the given orbital.

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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 = 3, which corresponds to an f orbital, ml can take values of -3, -2, -1, 0, +1, +2, and +3, resulting in a total of seven possible orientations.

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Related Practice

Textbook Question

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

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Textbook Question

A certain orbital of the hydrogen atom has n = 4 and l = 3. (b) What are the possible values of ms for the orbital?

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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

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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

Using Heisenberg's uncertainty principle, calculate the uncertainty in the position of (b) a proton moving at a speed of 15.00 { 0.012 * 104 m/s. (The mass of a proton is given in the table of fundamental constants in the inside cover of the text.)

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Textbook Question

Calculate the uncertainty in the position of (a) an electron moving at a speed of 13.00 ± 0.012 × 10⁵ m/s (b) a neutron moving at this same speed. (The masses of an electron and a neutron are given in the table of fundamental constants in the inside cover of the text.)

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