The shape of the S-orbital is

1. Analyze the question

The question asks for the geometric shape of the s-orbital in an atom. This is a fundamental concept in atomic structure and quantum chemistry, which frequently appears in JAMB Chemistry exams.

2. Explain the concept

In quantum mechanics, orbitals are regions in space where there is a high probability of finding an electron. These orbitals have specific shapes determined by the angular momentum quantum number ($l$):

• s-orbitals ($l=0$): These are spherically symmetrical around the nucleus.
• p-orbitals ($l=1$): These are dumbbell-shaped.
• d-orbitals ($l=2$): These are mostly double-dumbbell shaped.

Because the s-orbital is spherically symmetrical, the probability of finding an electron at a given distance from the nucleus is the same in all directions.

3. Show the solution

• The s-orbital is the simplest type of orbital.
• It is defined by the principal quantum number ($n$) and has no angular dependence.
• Geometrically, a shape that is uniform in all three dimensions ($x, y, z$ axes) is a sphere.
• Therefore, the electron cloud of an s-orbital is distributed in a spherical volume around the nucleus.

4. Identify the answer

Comparing our explanation to the given options:

• A. Elliptical (Incorrect - this relates to older models like Bohr-Sommerfeld)
• B. Spiral (Incorrect - this is not a shape of an orbital)
• C. Circular (Incorrect - a circle is 2D; an orbital is 3D)
• D. Spherical (Correct - this accurately describes the 3D shape)

5. Exam Tip

To remember orbital shapes, use the mnemonic "S-P-D":

• S = Spherical
• P = Propeller (or dumbbell)
• D = Double-dumbbell