/*! 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 88 Give the maximum number of elect... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 88

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. \(n=1, \ell=0, m_{\ell}=0\)

Short Answer

Expert verified
In summary: - a. There are 0 electrons. - b. There is 1 electron. - c. There are 10 electrons. - d. There are 0 electrons. - e. There are 2 electrons.

Step by step solution

01

Check validity of quantum numbers

Let's verify the quantum numbers' validity. Principle quantum number \(n\) should be a positive integer, meaning \(n=1,2,3,...\). Here, \(n=0\), which is not a valid value for the principle quantum number. Thus, the given quantum numbers are invalid.
02

Number of electrons

Since the given quantum numbers are invalid, there will be no electrons having these quantum numbers. b. \(n=2\), \(\ell=1\), \(m_{\ell}=-1\), \(m_{s}=-\frac{1}{2}\)
03

Check validity of quantum numbers

The given quantum numbers are valid with \(n=2\), \(\ell=1\), \(m_{\ell}=-1\) and \(m_{s}=-\frac{1}{2}\).
04

Number of electrons

Since we have valid quantum numbers, there is only one maximum electron (due to the unique combination of quantum numbers) that can have these quantum numbers. c. \(n=3\), \(m_{s}=+\frac{1}{2}\)
05

Check validity of quantum numbers

Principle quantum number \(n\) is valid. We are not given the values of \(\ell\) and \(m_{\ell}\), so let's find the maximum electrons for \(n=3\).
06

Number of electrons

Since \(n=3\), the various subshells will be \(0,1,2\). For each subshell: - \(\ell = 0\), there will be one orbital, that can accommodate \(2\) electrons with \(m_s = \frac{1}{2}\). - \(\ell = 1\), there will be three orbitals (\(m_\ell = -1, 0, 1\)), and each orbital can accommodate \(1\) electron with \(m_s = \frac{1}{2}\). So, a total of \(3\) electrons for this subshell. - \(\ell = 2\), there will be five orbitals (\(m_\ell = -2,-1,0,1,2\)), and each orbital can accommodate \(1\) electron with \(m_s = \frac{1}{2}\). So, a total of \(5\) electrons for this subshell. Adding electrons from all subshells, we get \(2+3+5 = 10\) electrons. d. \(n=2\), \(\ell=2\)
07

Check validity of quantum numbers

Here, the principle quantum number is valid, but the value of \(\ell\) is invalid as the maximum value of \(\ell\) should be \(n-1\). Since \(\ell = n > n-1\) for \(n=2\), the value of \(\ell\) is invalid.
08

Number of electrons

Since the given quantum numbers are invalid, there will be no electrons having these quantum numbers. e. \(n=1\), \(\ell=0\), \(m_{\ell}=0\)
09

Check validity of quantum numbers

In this case, the given quantum numbers are valid with \(n=1\), \(\ell=0\) and \(m_{\ell}=0\).
10

Number of electrons

Since we have valid quantum numbers, there is one orbital associated with these quantum numbers. This orbital can accommodate 2 electrons, one with spin \(+\frac{1}{2}\) and another with spin \(-\frac{1}{2}\). So, there can be a maximum of 2 electrons that can have these quantum numbers. In summary: - a. There are 0 electrons. - b. There is 1 electron. - c. There are 10 electrons. - d. There are 0 electrons. - e. There are 2 electrons.

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!

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

A certain microwave oven delivers 750 . watts \((\mathrm{J} / \mathrm{s})\) of power to a coffee cup containing 50.0 \(\mathrm{g}\) water at \(25.0^{\circ} \mathrm{C}\) . If the wave- length of microwaves in the oven is \(9.75 \mathrm{cm},\) how long does it take, and how many photons must be absorbed, to make the water boil? The specific heat capacity of water is 4.18 \(\mathrm{J} /^{\prime} \mathrm{C} \cdot \mathrm{g}\) and assume only the water absorbs the energy of the microwaves

The work function of an element is the energy required to remove an electron from the surface of the solid element. The work function for lithium is 279.7 kJ/mol (that is, it takes 279.7 kJ of energy to remove one mole of electrons from one mole of Li atoms on the surface of Li metal). What is the maximum wavelength of light that can remove an electron from an atom on the surface of lithium metal?

Francium, Fr, is a radioactive element found in some uranium minerals and is formed as a result of the decay of actinium. a. What are the electron configurations of francium and its predicted most common ion? b. It has been estimated that at any one time, there is only one (1.0) ounce of francium on earth. Assuming this is true, what number of francium atoms exist on earth? c. The longest-lived isotope of francium is \(^{223} \mathrm{Fr}\) . What is the total mass in grams of the neutrons in one atom of this isotope?

Predict the atomic number of the next alkali metal after francium and give its ground-state electron configuration.

Assume that a hydrogen atom's electron has been excited to the \(n=6\) level. How many different wavelengths of light can be emitted as this excited atom loses energy?
See all solutions

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Read Explanation

Kinetics

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Inorganic Chemistry

Read Explanation

Nuclear Chemistry

Read Explanation

Chemical Analysis

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.