Calculate the de Broglie wavelength of a 1.2-kg rock thrown with a speed of 6.0 m/s into a pond. Is this wavelength similar to that of the water waves pro- duced? Explain
Calculate the de Broglie wavelength of a 1.2-kg rock thrown with a speed of 6.0 m/s into a pond. Is this wavelength similar to that of the water waves pro- duced? Explain
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Question
![**Problem Statement: Calculating the de Broglie Wavelength of a Rock**
**Objective:**
Calculate the de Broglie wavelength of a 1.2-kg rock thrown with a speed of 6.0 m/s into a pond. Then, determine if this wavelength is similar to that of the water waves produced. Explain your reasoning.
---
**Explanation:**
To find the de Broglie wavelength, we use the de Broglie hypothesis, which states that any moving particle or object has an associated wavelength. The de Broglie wavelength \(\lambda\) is given by:
\[
\lambda = \frac{h}{p}
\]
where \(h\) is the Planck constant (\(6.626 \times 10^{-34} \, \text{Js}\)), and \(p\) is the momentum of the object.
The momentum \(p\) is given by:
\[
p = mv
\]
where \(m\) is the mass of the object (1.2 kg) and \(v\) is the velocity (6.0 m/s).
1. **Calculate the momentum:**
\[
p = 1.2 \, \text{kg} \times 6.0 \, \text{m/s} = 7.2 \, \text{kg m/s}
\]
2. **Calculate the de Broglie wavelength:**
\[
\lambda = \frac{6.626 \times 10^{-34} \, \text{Js}}{7.2 \, \text{kg m/s}}
\]
3. **Solve for \(\lambda\):**
\[
\lambda = \frac{6.626 \times 10^{-34}}{7.2} \approx 9.20 \times 10^{-35} \, \text{m}
\]
**Comparison to Water Waves:**
The wavelength calculated (\(9.20 \times 10^{-35} \, \text{m}\)) is incredibly small compared to typical wavelengths of water waves, which are usually several centimeters to several meters in length. Therefore, the de Broglie wavelength of the rock is minuscule and insignificant in the context of the water waves produced when the rock is thrown into the pond.
**Conclusion:**
The de Broglie wavelength of the rock (approximately \(9.20 \times 10^{-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F093e7116-3e01-49ad-9157-7a22a5caeb16%2F67d22d05-ceed-4f4f-afde-865826481dd5%2Fkjow8i_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement: Calculating the de Broglie Wavelength of a Rock**
**Objective:**
Calculate the de Broglie wavelength of a 1.2-kg rock thrown with a speed of 6.0 m/s into a pond. Then, determine if this wavelength is similar to that of the water waves produced. Explain your reasoning.
---
**Explanation:**
To find the de Broglie wavelength, we use the de Broglie hypothesis, which states that any moving particle or object has an associated wavelength. The de Broglie wavelength \(\lambda\) is given by:
\[
\lambda = \frac{h}{p}
\]
where \(h\) is the Planck constant (\(6.626 \times 10^{-34} \, \text{Js}\)), and \(p\) is the momentum of the object.
The momentum \(p\) is given by:
\[
p = mv
\]
where \(m\) is the mass of the object (1.2 kg) and \(v\) is the velocity (6.0 m/s).
1. **Calculate the momentum:**
\[
p = 1.2 \, \text{kg} \times 6.0 \, \text{m/s} = 7.2 \, \text{kg m/s}
\]
2. **Calculate the de Broglie wavelength:**
\[
\lambda = \frac{6.626 \times 10^{-34} \, \text{Js}}{7.2 \, \text{kg m/s}}
\]
3. **Solve for \(\lambda\):**
\[
\lambda = \frac{6.626 \times 10^{-34}}{7.2} \approx 9.20 \times 10^{-35} \, \text{m}
\]
**Comparison to Water Waves:**
The wavelength calculated (\(9.20 \times 10^{-35} \, \text{m}\)) is incredibly small compared to typical wavelengths of water waves, which are usually several centimeters to several meters in length. Therefore, the de Broglie wavelength of the rock is minuscule and insignificant in the context of the water waves produced when the rock is thrown into the pond.
**Conclusion:**
The de Broglie wavelength of the rock (approximately \(9.20 \times 10^{-
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