Ch.6 - Electronic Structure of Atoms

Brown - Chemistry: The Central Science 14th Edition

Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Non è quello che usi tu?Cambia libro di testo

Brown 14th Edition

Ch.6 - Electronic Structure of Atoms

Problema 10d

Capitolo 6, Problema 10d

The accompanying drawing shows a contour plot for a dyz orbital. Consider the quantum numbers that could potentially correspond to this orbital. (d) The probability density goes to zero along which of the following planes: xy, xz, or yz?

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Identify the type of orbital shown in the contour plot. The given plot is for a dyz orbital, which is a type of d orbital.

Recall the general shape and orientation of d orbitals. The dyz orbital has lobes oriented along the y and z axes.

Understand the concept of nodes in orbitals. Nodes are regions where the probability density of finding an electron is zero.

Determine the planes where the probability density goes to zero for the dyz orbital. For the dyz orbital, the nodes are along the xz plane.

Conclude that the probability density for the dyz orbital goes to zero along the xz plane.

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Quantum Numbers

Quantum numbers are sets of numerical values that describe the unique quantum state of an electron in an atom. They include the principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m_l), and spin quantum number (m_s). For a dyz orbital, the relevant quantum numbers are n, l=2 (for d orbitals), and m_l= -1 or +1, indicating the orientation of the orbital.

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02:55

Principal Quantum Number

Orbital Shapes and Probability Density

Orbitals are regions in an atom where there is a high probability of finding electrons. The shape of an orbital, such as the dyz orbital, is determined by its angular momentum quantum number (l). The contour plot illustrates the lobes of the dyz orbital, which are oriented along the y and z axes, indicating where the probability density is high, while the density is zero along the xz plane.

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Density Concepts

Nodes in Orbitals

Nodes are regions in an orbital where the probability density of finding an electron is zero. For the dyz orbital, there is a nodal plane along the xz plane, meaning that at this plane, the probability of finding an electron is zero. Understanding the concept of nodes is crucial for visualizing the spatial distribution of electrons in different orbitals.

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Radial Nodes Example

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The accompanying drawing shows a contour plot for a dyz orbital. Consider the quantum numbers that could potentially correspond to this orbital. (b) What is the value of the angular momentum quantum number, l?

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Four possible electron configurations for a nitrogen atom are shown below, but only one schematic represents the correct configuration for a nitrogen atom in its ground state. Which configurations violate the Pauli exclusion principle?

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Four possible electron configurations for a carbon atom are shown below, but only one schematic represents the correct configuration for a carbon atom in its ground state. Which one is the correct electron configuration?

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The accompanying drawing shows a contour plot for a dyz orbital. Consider the quantum numbers that could potentially correspond to this orbital. (c) What is the largest possible value of the magnetic quantum number, ml?

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The contour representation of one of the orbitals for the n = 3 shell of a hydrogen atom is shown here. (c) In which of the following ways would you modify this sketch if the value of the magnetic quantum number, ml, were to change? (i) It would be drawn larger, (ii) the number of lobes would change, (iii) the lobes of the orbital would point in a different direction, (iv) there would be no change in the sketch.

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