Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 9

(a) Evaluate the expressions \(2 \times 1,2 \times(1+3)\) \(2 \times(1+3+5),\) and \(2 \times(1+3+5+7)\) . (b) How do the atomic numbers of the noble gases relate to the numbers from part (a)? (c) What topic discussed in Chapter 6 is the source of the number \(" 2 "\) in the expressions in part (a)?

Short Answer

Expert verified
The evaluated expressions from part (a) are 2, 8, 18, and 32. These numbers are closely related to the atomic numbers of the noble gases, specifically Helium (2), Neon (10), Argon (18), and Krypton (36). The connection between these values may be related to the maximum number of electrons in specific energy levels, contributing to the stability of noble gases. However, without more context on Chapter 6, it's difficult to determine the exact significance of the number 2 in these expressions.

Step by step solution

01

Evaluate the expressions

For part (a), we need to evaluate the following expressions: \( 2 \times 1 \), \( 2 \times (1 + 3) \), \( 2 \times (1 + 3 + 5) \), and \( 2 \times (1 + 3 + 5 + 7) \) Let's start evaluating each expression one by one: 1. \( 2 \times 1 = 2 \) 2. \( 2 \times (1 + 3) = 2 \times 4 = 8 \) 3. \( 2 \times (1 + 3 + 5) = 2 \times 9 = 18 \) 4. \( 2 \times (1 + 3 + 5 + 7) = 2 \times 16 = 32 \) So, the evaluated expressions are 2, 8, 18, and 32.
02

Relate the expressions to the atomic numbers of noble gases

In part (b), we're supposed to find a connection between the values we got in the previous step (2, 8, 18, 32) and the atomic numbers of the noble gases. Let's list down the atomic numbers of the first few noble gases: 1. Helium (He) - 2 2. Neon (Ne) - 10 3. Argon (Ar) - 18 4. Krypton (Kr) - 36 We can see that there is a connection between the expressions' values and the atomic numbers of the noble gases. The atomic numbers of the noble gases are close to the evaluated expressions, except for Neon (10) and Krypton (36), which differ by 2 units each.
03

Identify the source of the number "2" in the expressions

In part (c), we have to discuss the significance of the number "2" in the expressions and how it relates to a topic in Chapter 6 (which hasn't been specified in the given context). Nevertheless, the number "2" has different significances in chemistry. For example, it could refer to the maximum number of electrons in the first energy level (1s orbital) or the stability of noble gases due to having completely filled energy levels. Without more information on the specific context of Chapter 6, we cannot pinpoint the exact significance of the number 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

You read the following statement about two elements \(\mathrm{X}\) and \(\mathrm{Y} :\) One of the elements is a good conductor of electricity, and the other is a semiconductor. Experiments show that the first ionization energy of \(\mathrm{X}\) is twice as great as that of Y. Which element has the greater metallic character?

Detailed calculations show that the value of \(Z_{\text { eff }}\) for the outermost electrons in Na and \(K\) atoms is \(2.51+\) and \(3.49+\) respectively. (a) What value do you estimate for \(Z_{\text { eff }}\) experienced by the outermost electron in both Na and K by assuming core electrons contribute 1.00 and valence electrons contribute 0.00 to the screening constant? (b) What values do you estimate for \(Z_{\text { eff }}\) using Slater's rules? (c) Which approach gives a more accurate estimate of \(Z_{\text { eff? }}\) (d) Does either method of approximation account for the gradual increase in \(Z_{\text { eff }}\) that occurs upon moving down a group? (e) Predict \(Z_{\text { eff }}\) for the outermost electrons in the Rb atom based on the calculations for Na and K.

For each of the following pairs, indicate which element has the smaller first ionization energy: (a) Ti, Ba; (b) Ag, Cu; (c) Ge, Cl; (d) Pb, Sb.

Arrange each of the following sets of atoms and ions, in order of increasing size: \((\mathbf{a}) \mathrm{Se}^{2-}, \mathrm{Te}^{2-}, \mathrm{Se} ;(\mathbf{b}) \mathrm{Co}^{3+}, \mathrm{Fe}^{2+}, \mathrm{Fe}^{3+};\) \((\mathbf{c}) \mathrm{Ca}, \mathrm{Ti}^{4+}, \mathrm{Sc}^{3+} ;(\mathbf{d}) \mathrm{Be}^{2+}, \mathrm{Na}^{+}, \mathrm{Ne}.\)

Arrange the following atoms in order of increasing effective nuclear charge experienced by the electrons in the \(n=3\) electron shell: \(\mathrm{K}, \mathrm{Mg}, \mathrm{P}, \mathrm{Rh} , \mathrm{Ti}.\)
See all solutions

Recommended explanations on Chemistry Textbooks

Organic Chemistry

Read Explanation

Physical Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Making Measurements

Read Explanation

Chemistry Branches

Read Explanation

Nuclear 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