Which of the following sketches best represents a 3d atomic orbital?

• A. A spherical region centered around the nucleus
• B. A cloverleaf-shaped region with four lobes centered around the nucleus
• C. A dumbbell-shaped region with two lobes along a single axis
• D. A toroidal (doughnut-shaped) region surrounding the nucleus

Answer: (B)

Verified step by step guidance

1. Recall that atomic orbitals are regions in space where there is a high probability of finding an electron. The shape of these orbitals depends on the quantum numbers, especially the angular momentum quantum number \( l \).
2. Understand that the \( s \)-orbitals (\( l = 0 \)) are spherical in shape, centered around the nucleus, representing a uniform probability distribution in all directions.
3. Recognize that the \( p \)-orbitals (\( l = 1 \)) have a dumbbell shape with two lobes oriented along one of the Cartesian axes (x, y, or z).
4. Know that the \( d \)-orbitals (\( l = 2 \)) have more complex shapes, including cloverleaf patterns with four lobes centered around the nucleus, as well as other shapes like a donut-shaped ring around a dumbbell.
5. Identify that a 3d atomic orbital specifically refers to one of the \( d \)-orbitals, which are typically represented by cloverleaf-shaped regions with four lobes, distinguishing them from spherical (s) or dumbbell (p) shapes.