Give the numerical values of n and l corresponding to each of the following orbital designations: (a) 3p (b) 2s (c) 4f

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Understand that the principal quantum number \( n \) indicates the energy level or shell of the electron. For the given orbital designation '3p', the number '3' represents the principal quantum number \( n \).

Recognize that the azimuthal quantum number \( l \) determines the shape of the orbital. The letter 'p' corresponds to \( l = 1 \).

Combine the information: for the '3p' orbital, \( n = 3 \) and \( l = 1 \).

Recall that the azimuthal quantum number \( l \) can take values from 0 to \( n-1 \). For \( n = 3 \), \( l \) can be 0, 1, or 2, which correspond to 's', 'p', and 'd' orbitals respectively.

Verify that the given designation '3p' correctly matches \( n = 3 \) and \( l = 1 \), confirming the orbital's energy level and shape.

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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 principal quantum number (n) indicates the energy level and size of the orbital, while the azimuthal quantum number (l) defines the shape of the orbital. Together, these numbers help in identifying the location and energy of electrons.

Principal Quantum Number (n)

The principal quantum number (n) is a positive integer that represents the main energy level of an electron in an atom. It can take values of 1, 2, 3, and so on, with higher values corresponding to higher energy levels and larger orbitals. For the 3p orbital, n is 3, indicating it is in the third energy level.

Azimuthal Quantum Number (l)

The azimuthal quantum number (l) determines the shape of the orbital and can take integer values from 0 to (n-1). Each value of l corresponds to a specific type of orbital: 0 for s, 1 for p, 2 for d, and 3 for f. For the 3p orbital, l is 1, indicating it has a p-shaped configuration.

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Textbook Question

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

Textbook Question

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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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.)

Textbook Question

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

Textbook Question

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

Textbook Question

How many unique combinations of the quantum numbers l and ml are there when (a) n = 1 (b) n = 5?