The contour representation of one of the orbitals for the n = 3 shell of a hydrogen atom is shown here. (a) What is the quantum number l for this orbital?

Verified step by step guidance

1. Identify the shape of the orbital from the image. The image shows a dumbbell-shaped orbital.
2. Recall that the dumbbell shape corresponds to a p-orbital.
3. Understand that p-orbitals have an angular momentum quantum number (l) of 1.
4. Since the principal quantum number (n) is given as 3, the possible values for the angular momentum quantum number (l) are 0, 1, and 2.
5. Conclude that for a p-orbital in the n=3 shell, the quantum number l is 1.

Key Concepts

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 include the principal quantum number (n), which indicates the energy level; the angular momentum quantum number (l), which describes the shape of the orbital; the magnetic quantum number (m_l), which specifies the orientation of the orbital; and the spin quantum number (m_s), which indicates the spin direction of the electron.

Angular Momentum Quantum Number (l)

The angular momentum quantum number (l) determines the shape of an electron's orbital and can take on integer values from 0 to n-1, where n is the principal quantum number. For example, if n=3, l can be 0, 1, or 2, corresponding to s, p, and d orbitals, respectively. The value of l also influences the energy and spatial distribution of the electron within the atom.

Orbital Shapes

Orbitals are regions in an atom where there is a high probability of finding electrons. The shape of an orbital is determined by the angular momentum quantum number (l). For instance, an l value of 0 corresponds to a spherical s orbital, l=1 corresponds to a dumbbell-shaped p orbital, and l=2 corresponds to more complex d orbitals. The image provided depicts a p orbital, which is indicative of l=1.