/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 78 In which of the following case w... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 78

In which of the following case would the probability of finding an electron residing in a dxy orbital be zero? a. \(\mathrm{xz}\) and \(\mathrm{yz}\)-planes b. \(\mathrm{xy}\) and \(\mathrm{yz}\)-planes c. Z-direction, \(\mathrm{yz}\) and \(\mathrm{xz}\)-planes d. \(\mathrm{xy}\) and \(\mathrm{xz}\)-planes

Short Answer

Expert verified
The probability is zero in case (a): 1xz3 and 1yz3-planes.

Step by step solution

01

Identify xy Orbital's Node Planes

The 1dxy3 orbital has node planes in the 1xz3 and 1yz3 planes. This means that there is a probability of zero of finding an electron on the node planes, or in simpler terms, the 1dxy3 orbital is symmetric about the xy-plane and changes sign as you move through the 1xz3 or 1yz3 planes.
02

Compare Node Planes with Options

Now, compare the node planes of the 1dxy3 orbital (i.e., 1xz3 and 1yz3 planes) with the provided answer options to see which corresponds to the node planes.
03

Identify Option Corresponding to Both Node Planes

Option (a) mentions the 1xz3 and 1yz3-planes, which precisely corresponds to the node planes of the 1dxy3 orbital. This means that the probability of finding an electron in the 1dxy3 orbital in these planes would be zero.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Node Planes
Node planes are particular areas in an atomic orbital where the probability of finding an electron is exactly zero. These planes are like invisible barriers or divides within an orbital.
Imagine an orbital as a space where electrons buzz around. Node planes slice through this space, pushing electrons out of certain paths.In a \(dxy\) orbital, these node planes are the \(xz\) and \(yz\) planes. The electrons cannot reside on these planes because the quantum mechanical equations predict zero likelihood there.
Thus, knowing where these planes are helps us predict where not to find electrons, which is quite useful when visualizing complex shapes of orbitals.
  • The \(dxy\) orbital is symmetric to the \(xy\)-plane.
  • The node planes \(xz\) and \(yz\) mean zero electron density.
  • This knowledge aids in understanding electron distributions within atoms.
Electron Probability
Electron probability in quantum chemistry refers to the chance of finding an electron within a particular area.With orbitals, however, we are dealing with shapes where these electrons might be at any given time.
This is not like a solar system, where electrons are planets circling a sun; rather, they act more like invisible clouds in certain regions.Each orbital's shape, including the \(dxy\), helps us visualize these probabilities. Through waves and equations, we calculate where electrons like to be.
  • In \(dxy\) orbitals, high probability areas exist in four lobes between the \(x\) and \(y\) axes.
  • Node planes \(xz\) and \(yz\) have zero probability.
  • Electrons are often in the areas where symmetry balances.
dxy Orbital Symmetry
The \(dxy\) orbital's symmetry tells us how to expect electron clouds to behave geometrically.This symmetry surrounds the \(xy\) plane, creating lobes that exist in quadrants where the axes meet.The symmetry makes these orbitals distinct from other types.Their balanced nature dictates that any movement across the node planes results in electron wave phase changes.
This means that as you cross from one side of a node plane to another, the sign of the wave function switches.
  • \(dxy\) is part of the five \(d\)-orbitals characterized by different nodes and symmetry.
  • The symmetry is crucial in predicting chemical bonding as it influences electron sharing between atoms.
  • Understanding its symmetry helps unravel molecular geometries and reactions.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In the following questions, two statements (Assertion) \(\mathrm{A}\) and Reason (R) are given. Mark a. If \(\mathrm{A}\) and \(\mathrm{R}\) both are correct and \(\mathrm{R}\) is the correct explanation of \(\mathrm{A}\) b. If \(\mathrm{A}\) and \(\mathrm{R}\) both are correct but \(\mathrm{R}\) is not the correct explanation of A c. A is true but \(\mathrm{R}\) is false d. A is false but \(\mathrm{R}\) is true e. \(\mathrm{A}\) and \(\mathrm{R}\) both are false (A): The shortest wavelength of transition of Lyman series is observed when electron jumps from orbit number, \(\mathrm{n}=\infty\) to \(\mathrm{n}=1\). \((\mathbf{R})\) : Since the wavelength of transition is given by \(\mathrm{hc} / \lambda=\Delta \mathrm{E}\)

Consider the following sets of quantum numbers: $$ \begin{array}{rrrrr} & \mathrm{n} & 1 & \mathrm{~m} & \mathrm{~s} \\ (1) & 3 & 0 & 0 & -1 / 2 \\ (2) & 2 & 2 & 2 & -1 / 2 \\ (3) & 4 & 3 & -2 & -1 / 2 \\ \text { (4) } & 1 & 0 & -1 & -1 / 2 \\ \text { (5) } & 3 & 2 & 3 & +1 / 2 \end{array} $$ Which of the following sets of quantum number is not possible? a. 2,3 and 4 b. \(1,2,3\) and 4 c. 2,4 and 5 d. 1 and 3

Which of the following is/are not correctly matched? a. \(\mathrm{e} / \mathrm{m}\) ratio of anode rays : Independent of gas in the discharge tube b. Radius of nucleus : (Mass number) \(^{12}\) c. Momentum of H-atom when electrons returns from \(\mathrm{n}=2\) to \(\mathrm{n}=1: 3 \mathrm{Rh} / 4\) d. Momentum of photon : Independent of wave length of light

In Bohr series of lines of hydrogen spectrum, the third line from the red end corresponds to which one of the following inter-orbit jumps of the electron for Bohr orbits in an atom of hydrogen? a. \(3 \rightarrow 2\) b. \(5 \rightarrow 2\) c. \(4 \rightarrow 1\) d. \(2 \rightarrow 5\)

(A): The angular momentum of d-orbital is \(\sqrt{6} \mathrm{~h} / 2 \pi\) (R): d-orbitals have double dumb-bell shaped except \(\mathrm{d} z^{2}\).
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Kinetics

Read Explanation

The Earths Atmosphere

Read Explanation

Organic Chemistry

Read Explanation

Physical Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.