Question

What overall shape do the \(2 p\) and \(3 p\) orbitals have? How do the \(2 p\) orbitals differ from the \(3 p\) orbitals? How are they similar?

Short answer

The 2p and 3p orbitals both have a dumbbell-like shape with three possible orientations: px, py, and pz. They are similar in shape and orientation due to both being a result of l=1. However, they differ in that 3p orbitals are in a higher energy level (n=3) than 2p orbitals (n=2), resulting in the 3p orbitals being larger and more diffuse. Additionally, 3p orbitals have a node, which 2p orbitals do not.

Step-by-step solution

1. Understanding Orbitals

Orbitals are regions around the nucleus of an atom where electrons are most likely to be found. The shape of an orbital is determined by the combination of the principal quantum number 'n' (which defines the energy level) and the azimuthal quantum number 'l' (which defines the shape). In the case of 2p and 3p orbitals, the p orbitals correspond to l=1. The main difference between the 2p and 3p orbitals is the principal quantum number (n=2 for 2p and n=3 for 3p).

2. Shape of p Orbitals

The p orbitals have a dumbbell-like shape along the x, y, or z-axis. There are three possible orientations for p orbitals: px, py, and pz, oriented along the x, y, and z-axis respectively.

3. Similarities between 2p and 3p Orbitals

The main similarities between the 2p and 3p orbitals are: 1. Both 2p and 3p orbitals have the same dumbbell-like shape. 2. Both have three possible orientations: px, py, and pz. 3. Both are a result of l=1 which corresponds to p orbitals.

4. Differences between 2p and 3p Orbitals

The main differences between the 2p and 3p orbitals are: 1. The 3p orbitals are in a higher energy level than the 2p orbitals, as the principal quantum number for 3p is n=3 while for 2p it is n=2. 2. The 3p orbitals are larger and more diffuse compared to the 2p orbitals, due to the higher energy level of 3p orbitals. 3. The 3p orbitals have a node, which 2p orbitals do not. Nodes are surfaces where the probability of finding an electron is zero.