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Compare the de Broglie wavelength of an electron moving at 1.30×107 miles per hour (5.81×10€ m/s) to that of a golf ball moving at 70.0 miles per hour (31.3 m/s) and a proton with a speed of 1.30×107 miles per hour (5.81×10€ m/s). glie

Compare the de Broglie wavelength of an electron moving at 1.30×107 miles per hour (5.81×10€ m/s) to that of a golf ball moving at 70.0 miles per hour (31.3 m/s) and a proton with a speed of 1.30×107 miles per hour (5.81×10€ m/s). glie

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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## Understanding de Broglie Wavelengths in Different Particles ### Introduction The image explores the de Broglie wavelength of various particles, including an electron, a golf ball, and a proton, each moving at specific speeds. The task involves comparing these wavelengths and associating them with regions of the electromagnetic spectrum. ### Key Concepts - **de Broglie Wavelength**: A fundamental concept in quantum mechanics, linking the wave-like and particle-like properties of matter. - **Electromagnetic Spectrum**: A range of all types of electromagnetic radiation. ### Comparison Details - **Electron** - **Mass**: \(9.11 \times 10^{-31}\) kg - **Velocity**: \(5.81 \times 10^6\) m/s - **Wavelength Calculation**: Requires determining which region it falls into. - **Golf Ball** - **Mass**: \(4.50 \times 10^{-2}\) kg - **Velocity**: 31.3 m/s - **Wavelength Calculation**: Assign its spectrum region accordingly. - **Proton** - **Mass**: \(1.67 \times 10^{-27}\) kg - **Velocity**: \(5.81 \times 10^6\) m/s - **Wavelength Calculation**: Determine its correct spectrum region. ### Electromagnetic Spectrum Regions - **Ultraviolet (A)**: \(10^{-8}\) to \(10^{-7}\) meters - **X-ray (B)**: \(10^{-11}\) to \(10^{-8}\) meters - **Gamma ray (C)**: \(10^{-16}\) to \(10^{-11}\) meters - **Smaller than \(10^{-20}\) meters (D)**: Wave properties undetectable, only particle-like behavior observed. ### Conclusion By calculating the de Broglie wavelengths of each particle and comparing their magnitude to the given ranges, you determine their respective regions in the electromagnetic spectrum. ### Diagram/Table The table in the image provides the mass, velocity, calculated wavelength, and the region of the spectrum for each particle, aiding the visual comparison of these properties.
Transcribed Image Text:## Understanding de Broglie Wavelengths in Different Particles ### Introduction The image explores the de Broglie wavelength of various particles, including an electron, a golf ball, and a proton, each moving at specific speeds. The task involves comparing these wavelengths and associating them with regions of the electromagnetic spectrum. ### Key Concepts - **de Broglie Wavelength**: A fundamental concept in quantum mechanics, linking the wave-like and particle-like properties of matter. - **Electromagnetic Spectrum**: A range of all types of electromagnetic radiation. ### Comparison Details - **Electron** - **Mass**: \(9.11 \times 10^{-31}\) kg - **Velocity**: \(5.81 \times 10^6\) m/s - **Wavelength Calculation**: Requires determining which region it falls into. - **Golf Ball** - **Mass**: \(4.50 \times 10^{-2}\) kg - **Velocity**: 31.3 m/s - **Wavelength Calculation**: Assign its spectrum region accordingly. - **Proton** - **Mass**: \(1.67 \times 10^{-27}\) kg - **Velocity**: \(5.81 \times 10^6\) m/s - **Wavelength Calculation**: Determine its correct spectrum region. ### Electromagnetic Spectrum Regions - **Ultraviolet (A)**: \(10^{-8}\) to \(10^{-7}\) meters - **X-ray (B)**: \(10^{-11}\) to \(10^{-8}\) meters - **Gamma ray (C)**: \(10^{-16}\) to \(10^{-11}\) meters - **Smaller than \(10^{-20}\) meters (D)**: Wave properties undetectable, only particle-like behavior observed. ### Conclusion By calculating the de Broglie wavelengths of each particle and comparing their magnitude to the given ranges, you determine their respective regions in the electromagnetic spectrum. ### Diagram/Table The table in the image provides the mass, velocity, calculated wavelength, and the region of the spectrum for each particle, aiding the visual comparison of these properties.
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