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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Identify the quantum numbers: n (principal quantum number), l (azimuthal quantum number), and ml (magnetic quantum number).

Check the allowed values for each quantum number: n must be a positive integer, l must be an integer from 0 to n-1, and ml must be an integer from -l to +l.

For each row in the table, verify if the given quantum numbers are allowed based on the rules.

If the quantum numbers are allowed, determine the corresponding orbital type (s, p, d, f, etc.) based on the value of l.

If the quantum numbers are not allowed, write 'not allowed'.

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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. They include the principal quantum number (n), which indicates the energy level; the azimuthal quantum number (l), which defines the shape of the orbital; and the magnetic quantum number (ml), which specifies the orientation of the orbital in space.

Principal Quantum Number (n)

The principal quantum number (n) indicates the main energy level of an electron in an atom. It can take positive integer values (1, 2, 3, ...), with higher values corresponding to higher energy levels and greater distances from the nucleus. The value of n also determines the maximum number of electrons that can occupy that energy level, given by the formula 2n².

Azimuthal Quantum Number (l)

The azimuthal quantum number (l) defines the shape of the electron's orbital and can take integer values from 0 to n-1 for each principal quantum number. Each value of l corresponds to a specific type of orbital: l=0 for s orbitals, l=1 for p orbitals, l=2 for d orbitals, and l=3 for f orbitals. This number is crucial for determining the angular momentum of the electron.

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Magnetic Quantum Number

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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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A certain orbital of the hydrogen atom has n = 4 and l = 2. 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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Sketch the shape and orientation of the following types of orbitals: (a) s, (b) p_z, (c) d_xy.

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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

(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?