Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 167

Consider the ground state of arsenic, As. How many electrons have \(\ell=1\) as one of their quantum numbers? How many electrons have \(m_{\ell}=0 ?\) How many electrons have \(m_{\ell}=+1 ?\)

Short Answer

Expert verified
In the ground state of arsenic, 15 electrons have \(\ell=1\) as one of their quantum numbers, 6 electrons have \(m_{\ell}=0\), and 6 electrons have \(m_{\ell}=+1\).

Step by step solution

01

Find the electron configuration of arsenic

To find the electron configuration of arsenic, we need to know its atomic number. Arsenic has an atomic number of 33, which means it has 33 electrons in its ground state. We can now fill the orbitals in ascending order of energy, following the Aufbau principle. The electron configuration of arsenic is: \[1s^22s^22p^63s^23p^64s^23d^{10}4p^3\]
02

Count electrons with \(\ell=1\)

Now, we have to find the number of electrons that have \(\ell =1\). The value \(\ell=1\) corresponds to the p-orbitals. In the electron configuration of arsenic, we have: 2p: 6 electrons 3p: 6 electrons 4p: 3 electrons Total number of electrons with \(\ell=1\) is: \(6+6+3 = 15\)
03

Count electrons with \(m_{\ell}=0\)

Next, we need to find the number of electrons with \(m_{\ell}=0\). The value \(m_\ell=0\) corresponds to those orbitals which are aligned along the z-axis. To find them, we'll look at the electron configuration. In p-orbitals with \(\ell=1\), \(m_\ell\) can be -1, 0, or +1. Since each p-orbital can hold 6 electrons, there will be 2 electrons in each \(m_\ell\) state. So, there are 2 electrons with \(m_\ell=0\) in each of the following orbitals: 2p, 3p, and 4p. Total number of electrons with \(m_{\ell}=0\): \(2+2+2 = 6\)
04

Count electrons with \(m_{\ell}=+1\)

Lastly, we need to find the number of electrons with \(m_{\ell}=+1\). As mentioned earlier, in p-orbitals with \(\ell=1\), \(m_\ell\) can be -1, 0, or +1. Similar to the previous step, there will be 2 electrons with \(m_\ell=+1\) in each of the following orbitals: 2p, 3p, and 4p. Total number of electrons with \(m_{\ell}=+1\): \(2+2+2 = 6\) So, in the ground state of arsenic: - 15 electrons have \(\ell=1\) as one of their quantum numbers. - 6 electrons have \(m_{\ell}=0\). - 6 electrons have \(m_{\ell}=+1\).

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

It takes 208.4 kJ of energy to remove 1 mole of electrons from an atom on the surface of rubidium metal. How much energy does it take to remove a single electron from an atom on the surface of solid rubidium? What is the maximum wavelength of light capable of doing this?

Mars is roughly 60 million km from Earth. How long does it take for a radio signal originating from Earth to reach Mars?

Determine the maximum number of electrons that can have each of the following designations: \(2 f, 2 d_{x y}, 3 p, 5 d_{y z},\) and 4\(p .\)

It takes 476 kJ to remove 1 mole of electrons from the atoms at the surface of a solid metal. What is the maximum wavelength of light that can remove a single electron from an atom at the surface of this solid metal?

Predict some of the properties of element 117 (the symbol is Uus, following conventions proposed by the International Union of Pure and Applied Chemistry, or IUPAC). a. What will be its electron configuration? b. What element will it most resemble chemically? c. What will be the formula of the neutral binary compounds it forms with sodium, magnesium, carbon, and oxygen? d. What oxyanions would you expect Uus to form?
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Reactions

Read Explanation

Chemical Analysis

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Kinetics

Read Explanation

Organic Chemistry

Read Explanation

Making Measurements

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