General Chemistry Exam 2 Study Guidance (CHM 2045, Chapters 5–8)

Q9. Which labels, in the order they are written, best describe the orbitals in the order shown to the right?

Background

Topic: Atomic Orbitals and Quantum Numbers

This question tests your understanding of the shapes and labels of atomic orbitals, specifically the p and d orbitals, and how their principal quantum number (n) and angular momentum quantum number (l) relate to their appearance and energy levels.

Key Terms and Concepts:

• Principal Quantum Number (n): Indicates the main energy level or shell (e.g., n = 2, 3, 4, ...).

• Angular Momentum Quantum Number (l): Determines the shape of the orbital (l = 0 for s, 1 for p, 2 for d, etc.).

• p Orbitals: Dumbbell-shaped, each energy level n ≥ 2 has three p orbitals (2p, 3p, 4p, ...).

• d Orbitals: More complex shapes, each energy level n ≥ 3 has five d orbitals (3d, 4d, 5d, ...).

Step-by-Step Guidance

1. Observe the image: The orbitals shown have a characteristic dumbbell shape with an increasing size from left to right. This is typical of p or d orbitals as n increases.

   

2. Recall that for a given type of orbital (e.g., p or d), the size increases as the principal quantum number (n) increases. The smallest is the lowest n, and the largest is the highest n.

3. Consider the possible quantum numbers: For p orbitals, n starts at 2 (2p, 3p, 4p, ...). For d orbitals, n starts at 3 (3d, 4d, 5d, ...).

4. Match the increasing size to the increasing principal quantum number. The leftmost is the smallest (lowest n), and the rightmost is the largest (highest n).

Try solving on your own before revealing the answer!

Final Answer: (3) 3d, 4d, 5d

The orbitals shown are d orbitals (due to their shape), and their size increases with n. Thus, from left to right, they are 3d, 4d, and 5d.