Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 53

Calculate the de Broglie wavelength for each of the following. a. an electron with a velocity \(10 . \%\) of the speed of light b. a tennis ball \((55 \mathrm{~g})\) served at \(35 \mathrm{~m} / \mathrm{s}(\sim 80 \mathrm{mi} / \mathrm{h})\)

Short Answer

Expert verified
The de Broglie wavelength for an electron traveling at 10% of the speed of light is approximately \(2.43 \times 10^{-12}\) m, and the de Broglie wavelength for a tennis ball served at 35 m/s is approximately \(3.43 \times 10^{-34}\) m.

Step by step solution

01

Part a: Electron at 10% speed of light

Given: - velocity of electron, \(v = 0.10c = 0.10 \times 3 \times 10^8 \, \text{m}/\text{s}\) (since 10% of the speed of light) - mass of electron, \(m_e = 9.11 \times 10^{-31} \, \text{kg}\) - Planck's constant, \(h = 6.63 \times 10^{-34} \, \text{J} \cdot \text{s}\) Calculating the wavelength using the de Broglie's formula: \(λ = \frac{h}{mv}\) Plug in the values: \(λ = \frac{6.63 \times 10^{-34} \, \text{J} \cdot \text{s}}{(9.11 \times 10^{-31} \text{kg})(0.10 \times 3 \times 10^8 \, \text{m}/\text{s})}\) Calculate: \(λ = 2.43 \times 10^{-12} \, \text{m}\) So, the de Broglie wavelength for an electron with a velocity of 10% of the speed of light is approximately \(2.43 \times 10^{-12}\) m.
02

Part b: Tennis ball served at 35 m/s

Given: - mass of tennis ball, \(m_t = 55 \, \text{g} = 0.055 \, \text{kg}\) - velocity of tennis ball, \(v = 35 \, \text{m}/\text{s}\) - Planck's constant, \(h = 6.63 \times 10^{-34} \, \text{J} \cdot \text{s}\) Calculating the wavelength using the de Broglie's formula: \(λ = \frac{h}{mv}\) Plug in the values: \(λ = \frac{6.63 \times 10^{-34} \, \text{J} \cdot \text{s}}{(0.055 \, \text{kg})(35\, \text{m}/\text{s})}\) Calculate: \(λ = 3.43 \times 10^{-34} \, \text{m}\) So, the de Broglie wavelength for a tennis ball served at 35 m/s is approximately \(3.43 \times 10^{-34}\) m.

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

Valence electrons are those electrons in the outermost principal quantum level (highest \(n\) level) of an atom in its ground state. Groups \(1 \mathrm{~A}\) to 8 A have from 1 to 8 valence electrons. For each group of the representative elements (1A-8A), give the number of valence electrons, the general valence electron configuration, a sample element in that group, and the specific valence electron configuration for that element.

Octyl methoxycinnamate and oxybenzone are common ingredients in sunscreen applications. These compounds work by absorbing ultraviolet (UV) B light (wavelength \(280-320 \mathrm{~nm}\) ), the UV light most associated with sunburn symptoms. What frequency range of light do these compounds absorb?

Three elements have the electron configurations \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2}\), \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4}\), and \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2}\). The first ionization en- ergies of these elements (not in the same order) are \(0.590,0.999\), and \(0.738 \mathrm{MJ} / \mathrm{mol}\). The atomic radii are 104,160 , and \(197 \mathrm{pm}\). Identify the three elements, and match the appropriate values of ionization energy and atomic radius to each configuration. Complete the following table with the correct information.

Which of the following statements is(are) true? a. \(\mathrm{F}\) has a larger first ionization energy than does \(\mathrm{Li}\). b. Cations are larger than their parent atoms. c. The removal of the first electron from a lithium atom (electron configuration is \(1 s^{2} 2 s^{1}\) ) is exothermic - that is, removing this electron gives off energy. d. The He atom is larger than the \(\mathrm{H}^{+}\) ion. e. The \(\mathrm{Al}\) atom is smaller than the \(\mathrm{Li}\) atom.

The elements Cu, O, La, Y, Ba, Tl, and Bi are all found in high-temperature ceramic superconductors. Write the expected electron configuration for these atoms.
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

Kinetics

Read Explanation

Inorganic Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Ionic and Molecular Compounds

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