Ch.7 - Quantum-Mechanical Model of the Atom

Problem 64

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Chapter 7, Problem 64

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

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Understand that d orbitals are a set of five orbitals in each energy level, starting from n=3 (3d orbitals).

Recognize that the 3d orbitals consist of five shapes: d_{xy}, d_{yz}, d_{zx}, d_{x^2-y^2}, and d_{z^2}. These orbitals have different orientations in space.

Sketch the 3d orbitals: d_{xy}, d_{yz}, and d_{zx} have lobes between the axes, d_{x^2-y^2} has lobes along the x and y axes, and d_{z^2} has a unique shape with a donut-shaped ring around the z-axis.

Note that the 4d orbitals are similar in shape to the 3d orbitals but are larger in size due to the higher principal quantum number (n=4), which means they are further from the nucleus.

Understand that the energy of the 4d orbitals is higher than that of the 3d orbitals, and they have more nodes, which are regions where the probability of finding an electron is zero.

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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, including s, p, d, and f orbitals. Each type of orbital has a distinct shape and energy level, influencing the arrangement of electrons in an atom.

Quantum Numbers

Quantum numbers are numerical values that describe the unique quantum state of an electron in an atom. The principal quantum number (n) indicates the energy level, while the azimuthal quantum number (l) defines the shape of the orbital. For d orbitals, l equals 2, and for f orbitals, l equals 3, which affects their spatial orientation and energy.

Differences Between 3d and 4d Orbitals

The 3d orbitals are found in the third energy level (n=3) and have a lower energy compared to the 4d orbitals, which are in the fourth energy level (n=4). The 4d orbitals are more complex in shape and have a higher energy due to their position in a higher principal energy level, leading to differences in electron distribution and chemical behavior.

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The greater the interaction between the metal and its ligands then the greater the energy of its d orbitals

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Textbook Question

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

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

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

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Open Question

An electron in a hydrogen atom is excited with electrical energy to an excited state with n = 2. The atom then emits a photon. What is the value of n for the electron after the emission?

Textbook Question

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

According to the quantum-mechanical model for the hydrogen atom, which electron transition produces light with the longer wavelength: 2p to 1s or 3p to 1s?