2.5 Shapes of Orbitals

This topic describes the shapes of s, p, d, and f orbitals. It also introduces free radicals as species with unpaired electrons.

Definition

Orbital: The region in space where the probability of finding an electron is maximum.

Free Radical: An atom or molecule with an unpaired electron or electrons in its outer shell.

Main Idea

Different orbitals have different shapes in three-dimensional space. The shape of an orbital depends on the azimuthal quantum number (l). The s orbital is spherical, p orbitals are dumbbell-shaped, d orbitals are mostly cloverleaf-shaped, and f orbitals have complicated shapes. Free radicals are species with unpaired electrons, making them highly reactive.

Core Concept

• l = 0 (s orbital): Spherically symmetrical
• l = 1 (p orbital): Dumbbell-shaped (two lobes)
• l = 2 (d orbital): Cloverleaf-shaped (four lobes), except d_z²
• l = 3 (f orbital): Complicated shapes

Detailed Explanation

Shapes of Orbitals

• Spherically symmetrical.
• The probability of finding the electron is the same in all directions at a given distance from the nucleus.

• Dumbbell-shaped (also called sausage-shaped).
• Has two lobes on opposite sides of the nucleus.
• There are three p orbitals: p_x, p_y, p_z, oriented along the x, y, and z axes.

• Cloverleaf-shaped (four lobes).
• Exception: d_z² has a different shape (a doughnut with two lobes along the z-axis).
• There are five d orbitals: d_xy, d_yz, d_xz, d_x²-y², d_z².

• Complicated shapes.
• There are seven f orbitals.

Summary Table

Free Radicals

• A free radical is an atom or molecule with an unpaired electron or electrons in its outer shell.
• This makes it highly reactive and capable of immediate reactions.
• They are activated atoms or molecules.

• The electronic configuration of free radicals is the same as those of atoms.
• Example: Cl, CH₃, Br

Example: - The electronic configuration of a chloride free radical is the same as that of a chlorine atom, but they are shown by a dot on them (e.g., Cl·).

Intermediate Level

Shapes of Orbitals

Number of Orbitals

• s: 1 orbital
• p: 3 orbitals (p_x, p_y, p_z)
• d: 5 orbitals (d_xy, d_yz, d_xz, d_x²-y², d_z²)
• f: 7 orbitals

Free Radicals

• Definition: Atom or molecule with an unpaired electron.
• Properties: Highly reactive, capable of immediate reactions.
• Examples: Cl·, CH₃·, Br·
• Electronic configuration: Same as the atom, but with a dot to indicate the unpaired electron.

Important Points

• 1. Orbital = region of maximum probability of finding an electron.
• 2. s orbital: spherical.
• 3. p orbital: dumbbell-shaped (two lobes).
• 4. d orbital: cloverleaf-shaped (four lobes), except d_z².
• 5. f orbital: complicated shapes.
• 6. Free radical: atom or molecule with an unpaired electron.
• 7. Free radicals are highly reactive.
• 8. Electronic configuration of free radicals is the same as that of atoms.

Remember

• - s orbital: Spherical
• - p orbital: Dumbbell
• - d orbital: Cloverleaf (except d_z²)
• - f orbital: Complicated
• - Free radical: Unpaired electron → highly reactive
• - Examples: Cl·, CH₃·, Br·

Common Mistakes

• 1. Thinking all d orbitals are cloverleaf-shaped: d_z² is an exception.
• 2. Confusing orbitals with shells: Orbitals are regions within shells.
• 3. Forgetting that free radicals have unpaired electrons: This makes them highly reactive.
• 4. Mixing up the number of orbitals: s=1, p=3, d=5, f=7.

Quick Revision

• Orbital = region of maximum probability of finding an electron.
• s orbital: spherical.
• p orbital: dumbbell-shaped (two lobes).
• d orbital: cloverleaf-shaped (four lobes), except d_z².
• f orbital: complicated shapes.
• Free radical: atom or molecule with an unpaired electron.
• Free radicals are highly reactive.
• Electronic configuration of free radicals is the same as that of atoms.

60-Second Revision

• s orbital: Spherical
• p orbital: Dumbbell
• d orbital: Cloverleaf (except d_z²)
• f orbital: Complicated
• Free radical: Unpaired electron → highly reactive
• Examples: Cl·, CH₃·, Br·

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