Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Problem 6

The value of the ionization energy of He given in Table 1 is described as being consistent with two electrons in a "shell" approximately the same distance from the nucleus as the one electron in H. Use the Coulombic Potential Energy equation, \(V=\frac{\mathrm{kq}_{1} \mathrm{q}_{2}}{\mathrm{~d}}\) to explain how this conclusion can be reached. Hint: recall the relationship between \(V\) and \(\mathrm{IE}_{1}\).

Short Answer

Expert verified
The ionization energy of Helium is twice that of Hydrogen, as it has two electrons approximately at the same distance from the nucleus as Hydrogen's one electron. This complies with the Coulombic Potential Energy equation, confirming the assertion from the table.

Step by step solution

01

Identifying Variables in Ionization Energy Context

Initially, the concept of ionization energy needs to be identified. Ionization energy (\(IE_1\)) is the energy required to remove an electron from an atom or an ion. In this case, the ionization energy of He (Helium) will be twice that of H (Hydrogen) because He has two electrons compared to one electron in H. This is due to the analogy that both electrons in He are at the same distance from the nucleus as the one electron in H.
02

Applying Coulombic Potential Energy Equation

Now, the Coulombic potential energy equation, \(V = \frac{kq_1q_2}{d}\), where \(V\) is potential energy, \(q_1\) and \(q_2\) are charges (in this case, of electrons and nucleus), \(k\) is Coulomb's constant, and \(d\) is the distance between the charges, needs to be applied. Since for both H and He the distance from the nucleus is the same and charges are also similar, the potential energy for both will be the same. The charges here would be the charge of electron and charge of nucleus.
03

Connecting Ionization Energy and Potential Energy

Understanding that the potential energy (\(V\)) is related to the ionization energy (\(IE_1\)) will help draw a conclusion. A lower potential energy implies a higher ionization energy as it would take more energy to remove the electron from the atom. Since both H and He have the same potential energy as per the Coulombic equation, He should theoretically have twice the ionization energy of H because it has twice the electrons of H.

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

Using grammatically correct English sentences: a) provide a possible explanation for why \(\mathrm{IE}_{1}\) for \(\mathrm{He}\) is greater than \(\mathrm{IE}_{1}\) for \(\mathrm{H}\). b) provide a possible explanation for why \(\mathrm{IE}_{1}\) for \(\mathrm{Li}\) is less than \(\mathrm{IE}_{1}\) for He.

Predict the relationship between \(\mathrm{IE}_{1}\) and atomic number by making a rough graph of IE \(_{1}\) vs. atomic number. DO NOT PROCEED TO THE NEXT PAGE UNTIL YOU HAVE COMPLETED THIS GRAPH.

Is the amount of energy required to remove one of the electrons from the first shell of Li greater than, less than, or equal to the \(\mathrm{IE}_{1}\) for Li? Explain your reasoning.

For atoms with many electrons, not all electrons are at the same distance from the nucleus. In this case, which electron would have the lowest ionization energy: the electron that is closest to the nucleus or the electron that is farthest from the nucleus? Explain.

Recall that the IE of \(\mathrm{H}\) is \(1.31 \mathrm{MJ} / \mathrm{mole}\). If all three electrons in Li were in the first shell at a distance equal to that of hydrogen, which of the following values would be the better estimate of the IE of Li: 3.6 MJ/mole or 0.6 MJ/mole? Explain.
See all solutions

Recommended explanations on Chemistry Textbooks

Inorganic Chemistry

Read Explanation

Physical Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Making Measurements

Read Explanation

Nuclear Chemistry

Read Explanation

Chemistry Branches

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