Compare the de Broglie wavelength of a golf ball moving at 70.0 miles per hour (31.3 m/s) to that of an alpha particle moving at 3.40x107 miles per hour (1.52x107 m/s) and a proton with a speed of 1.30x107 miles per hour (5.81×106 m/s). Wavelength Region Particle golf ball alpha particle proton Mass (kg) 0.0450 6.64 x 10-27 1.67 x 10-27 Velocity (m/s) 31.3 1.52 × 107 5.81 x 106 ultraviolet (10-8 to 10-7m) X-ray (10-11 to 10-8 m) gamma (10-16 to 10-¹1 m) smaller than 10-20 m
Compare the de Broglie wavelength of a golf ball moving at 70.0 miles per hour (31.3 m/s) to that of an alpha particle moving at 3.40x107 miles per hour (1.52x107 m/s) and a proton with a speed of 1.30x107 miles per hour (5.81×106 m/s). Wavelength Region Particle golf ball alpha particle proton Mass (kg) 0.0450 6.64 x 10-27 1.67 x 10-27 Velocity (m/s) 31.3 1.52 × 107 5.81 x 106 ultraviolet (10-8 to 10-7m) X-ray (10-11 to 10-8 m) gamma (10-16 to 10-¹1 m) smaller than 10-20 m
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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![**Educational Website Content: Comparing the de Broglie Wavelengths**
The de Broglie wavelength is an important concept in quantum mechanics that helps us understand the wave-like properties of particles. In this exercise, we compare the de Broglie wavelengths of a golf ball, an alpha particle, and a proton moving at different speeds.
**Data Table:**
| Particle | Mass (kg) | Velocity (m/s) | Wavelength | Region |
|-------------------|----------------------|--------------------|------------|-------------------------|
| Golf ball | 0.0450 | 31.3 | | |
| Alpha particle | \(6.64 \times 10^{-27}\) | \(1.52 \times 10^7\) | | |
| Proton | \(1.67 \times 10^{-27}\) | \(5.81 \times 10^6\) | | |
**Velocity Comparison:**
- Golf ball: 31.3 m/s (equivalent to 70.0 miles/hour).
- Alpha particle: \(1.52 \times 10^7\) m/s.
- Proton: \(5.81 \times 10^6\) m/s.
**Dropdown Menu for Wavelength Region:**
- Ultraviolet (\(10^{-8}\) to \(10^{-7}\) m)
- X-ray (\(10^{-11}\) to \(10^{-8}\) m)
- Gamma (\(10^{-16}\) to \(10^{-11}\) m)
- Smaller than \(10^{-20}\) m
**Instructions:**
Calculate the de Broglie wavelength for each particle using the formula:
\[ \lambda = \frac{h}{mv} \]
Where \( \lambda \) is the wavelength, \( h \) is Planck’s constant (\(6.626 \times 10^{-34} \, \text{m}^2 \text{kg/s}\)), \( m \) is the mass, and \( v \) is the velocity.
**Suggestions:**
- After calculating the wavelengths, determine the region in which each wavelength falls using the provided dropdown options.
- Submit your answers to check if they are correct.
**Actionable Steps:**
- Click "Submit Answer" to receive feedback.
- If needed, use the "Retry Entire Group" option](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F330c71d2-fea0-4f1b-83ac-8ba3f7b05042%2Faf4b8d2f-23d2-402a-b7b3-885392cd74e7%2F2a88h_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Website Content: Comparing the de Broglie Wavelengths**
The de Broglie wavelength is an important concept in quantum mechanics that helps us understand the wave-like properties of particles. In this exercise, we compare the de Broglie wavelengths of a golf ball, an alpha particle, and a proton moving at different speeds.
**Data Table:**
| Particle | Mass (kg) | Velocity (m/s) | Wavelength | Region |
|-------------------|----------------------|--------------------|------------|-------------------------|
| Golf ball | 0.0450 | 31.3 | | |
| Alpha particle | \(6.64 \times 10^{-27}\) | \(1.52 \times 10^7\) | | |
| Proton | \(1.67 \times 10^{-27}\) | \(5.81 \times 10^6\) | | |
**Velocity Comparison:**
- Golf ball: 31.3 m/s (equivalent to 70.0 miles/hour).
- Alpha particle: \(1.52 \times 10^7\) m/s.
- Proton: \(5.81 \times 10^6\) m/s.
**Dropdown Menu for Wavelength Region:**
- Ultraviolet (\(10^{-8}\) to \(10^{-7}\) m)
- X-ray (\(10^{-11}\) to \(10^{-8}\) m)
- Gamma (\(10^{-16}\) to \(10^{-11}\) m)
- Smaller than \(10^{-20}\) m
**Instructions:**
Calculate the de Broglie wavelength for each particle using the formula:
\[ \lambda = \frac{h}{mv} \]
Where \( \lambda \) is the wavelength, \( h \) is Planck’s constant (\(6.626 \times 10^{-34} \, \text{m}^2 \text{kg/s}\)), \( m \) is the mass, and \( v \) is the velocity.
**Suggestions:**
- After calculating the wavelengths, determine the region in which each wavelength falls using the provided dropdown options.
- Submit your answers to check if they are correct.
**Actionable Steps:**
- Click "Submit Answer" to receive feedback.
- If needed, use the "Retry Entire Group" option
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