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Ch.6 - Electronic Structure of Atoms
Brown - Chemistry: The Central Science 14th Edition
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Tutti i libri di testoBrown 14th EditionCh.6 - Electronic Structure of AtomsProblema 59a
Capitolo 6, Problema 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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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.
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Principal Quantum Number

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.
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Principal Quantum Number

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

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Give the numerical values of n and l corresponding to each of the following orbital designations: (d) 5d.

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Give the values for n, l, and ml for (a) each orbital in the 3p subshell, (b) each orbital in the 4f subshell.

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