Ch.8 - The Quantum-Mechanical Model of the Atom

Tro - Chemistry: A Molecular Approach 5th Edition

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Tro 5th Edition

Ch.8 - The Quantum-Mechanical Model of the Atom

Problem 63

Chapter 8, Problem 63

Sketch the 1s and 2p orbitals. How do the 2s and 3p orbitals differ from the 1s and 2p orbitals?

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Step 1: The 1s orbital is the simplest of all the orbitals. It is spherical in shape and centered around the nucleus. The electron cloud density is evenly distributed in all directions.

Step 2: The 2p orbital is different from the 1s orbital. It has two lobes on opposite sides of the nucleus, with a node (a region of zero electron density) at the nucleus. The 2p orbital can exist in three orientations in space, corresponding to the three axes (x, y, and z).

Step 3: The 2s orbital, like the 1s orbital, is spherical. However, it is larger than the 1s orbital and contains a node. This means that there is a region inside the 2s orbital where there is zero probability of finding an electron.

Step 4: The 3p orbital is similar to the 2p orbital in shape, but it is larger and contains two nodes. Like the 2p orbital, it also has three orientations in space.

Step 5: In summary, as the principal quantum number (n) increases, the size of the orbital increases and the number of nodes also increases. The shape of the s orbitals is always spherical, while the p orbitals have a dumbbell shape.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Atomic Orbitals

Atomic orbitals are regions in an atom where there is a high probability of finding electrons. They are defined by quantum numbers and come in various shapes, such as spherical (s orbitals) and dumbbell-shaped (p orbitals). The 1s orbital is the simplest, being spherical, while p orbitals have a more complex shape, indicating the directional nature of electron density.

Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and the electrons in them. The principal quantum number (n) indicates the energy level and size of the orbital, while the angular momentum quantum number (l) defines the shape. For example, 1s has n=1 and l=0, while 2p has n=2 and l=1, showing how orbitals differ in energy and shape.

Energy Levels and Electron Configuration

Energy levels refer to the fixed energies that electrons can have in an atom, with lower levels being closer to the nucleus. As n increases, the energy and size of the orbitals increase. The 2s and 3p orbitals differ from the 1s and 2p orbitals in their energy levels and spatial distribution, affecting how electrons are arranged in an atom and influencing chemical properties.

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Determine whether each transition in the hydrogen atom corresponds to absorption or emission of energy. a. n = 3 → n = 1 b. n = 2 → n = 4 c. n = 4 → n = 3

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Which set of quantum numbers cannot occur together to specify an orbital? a. n = 2, l = 1, m_l = -1 b. n = 3, l = 2, m_l = 0 c. n = 3, l = 3, m_l = 2 d. n = 4, l = 3, m_l = 0

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Which combinations of n and l represent real orbitals, and which do not exist? a. 1s b. 2p c. 4s d. 2d

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Sketch the 3d orbitals. How do the 4d orbitals differ from the 3d orbitals?