Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Problem 95

In the ground state of mercury, Hg, a. how many electrons occupy atomic orbitals with \(n=3 ?\) b. how many electrons occupy \(d\) atomic orbitals? c. how many electrons occupy \(p_{z}\) atomic orbitals? d. how many electrons have spin "up" \(\left(m_{s}=+\frac{1}{2}\right) ?\)

Short Answer

Expert verified
There are \(18\) electrons occupying orbitals with n=3, \(30\) electrons occupying d orbitals, \(8\) electrons occupying p_z atomic orbitals, and \(40\) electrons with spin "up" (m_s = +1/2) in the ground state of mercury (Hg).

Step by step solution

01

a. Electrons occupying orbitals with n=3

To find the number of electrons in orbitals with n=3, we need to count all the electrons in the 3s, 3p, and 3d orbitals. From the electronic configuration, we can see that: 3s: 2 electrons, 3p: 6 electrons, 3d: 10 electrons. Hence, there are 2 + 6 + 10 = \(18\) electrons occupying orbitals with n=3.
02

b. Electrons occupying d orbitals

To determine the number of electrons in d orbitals, we can examine the electronic configuration and sum up the electrons in the 3d, 4d, and 5d orbitals: 3d: 10 electrons, 4d: 10 electrons, 5d: 10 electrons. The total number of electrons in d orbitals is 10 + 10 + 10 = \(30\) electrons.
03

c. Electrons occupying p_z orbitals

The p_z orbitals are a subset of the p orbitals, and there is one p_z orbital in each p subshell. Since each orbital can hold a maximum of 2 electrons, there will be 2 electrons in the 2p_z, 3p_z, 4p_z, and 5p_z orbitals. Therefore, there are \(4\) sets of 2 electrons for a total of \(8\) electrons occupying p_z atomic orbitals.
04

d. Electrons with spin "up" (m_s = +1/2)

Finally, to determine the number of electrons with spin "up" (m_s = +1/2), we can assume that, in each orbital, one electron has spin "up" and the other has spin "down". Since there are 80 electrons in mercury, half (40) will have spin "up" and half (40) will have spin "down". Thus, there are \(40\) electrons with spin "up" (m_s = +1/2).

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Identify the following elements. a. An excited state of this element has the electron configuration \(1 s^{2} 2 s^{2} 2 p^{5} 3 s^{1}\). b. The ground-state electron configuration is \([\mathrm{Ne}] 3 s^{2} 3 p^{4}\). c. An excited state of this element has the electron configuration \([\mathrm{Kr}] 5 s^{2} 4 d^{6} 5 p^{2} 6 s^{1}\). d. The ground-state electron configuration contains three unpaired \(6 p\) electrons.

How many orbitals in an atom can have the designation \(5 p,\) \(3 d_{z}, 4 d, n=5, n=4 ?\)

One bit of evidence that the quantum mechanical model is "correct" lies in the magnetic properties of matter. Atoms with unpaired electrons are attracted by magnetic fields and thus are said to exhibit paramagnetism. The degree to which this effect is observed is directly related to the number of unpaired electrons present in the atom. Consider the ground-state electron configurations for Li, N, Ni, Te, Ba, and Hg. Which of these atoms would be expected to be paramagnetic, and how many unpaired electrons are present in each paramagnetic atom?

Give the maximum number of electrons in an atom that can have these quantum numbers: a. \(n=0, \ell=0, m_{\ell}=0\) b. \(n=2, \ell=1, m_{\ell}=-1, m_{s}=-\frac{1}{2}\) c. \(n=3, m_{s}=+\frac{1}{2}\) d. \(n=2, \ell=2\) e. \(n=1, \ell=0, m_{\ell}=0\)

Answer the following questions, assuming that \(m_{s}\) could have three values rather than two and that the rules for \(n, \ell,\) and \(m_{\ell}\) are the normal ones. a. How many electrons would an orbital be able to hold? b. How many elements would the first and second periods in the periodic table contain? c. How many elements would be contained in the first transition metal series? d. How many electrons would the set of \(4 f\) orbitals be able to hold?
See all solutions

Recommended explanations on Chemistry Textbooks

The Earths Atmosphere

Read Explanation

Inorganic Chemistry

Read Explanation

Making Measurements

Read Explanation

Organic Chemistry

Read Explanation

Chemical Reactions

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.

Sign-up for free