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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Question
How can we find out the maximum mass of an object traveling at 451m ?
![**Title: Exploring the de Broglie Wavelength in Chemistry**
**Introduction to de Broglie Wavelengths**
In the study of quantum mechanics within chemistry, we often encounter the concept of the de Broglie wavelength, which is used to describe the wave-like behavior of particles.
**Problem Statement**
Consider an experiment where the smallest measurable wavelength is 0.890 femtometers (fm). Our goal is to determine the maximum mass of an object for which the de Broglie wavelength is observable for an object traveling at a speed of 451 meters per second (m/s).
**Calculation**
To find the maximum mass \( m \) (in kilograms) where the de Broglie wavelength is observable, use the de Broglie wavelength formula:
\[ \lambda = \frac{h}{mv} \]
Where:
- \( \lambda \) is the wavelength (0.890 fm or \( 0.890 \times 10^{-15} \) meters).
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \) kg m\(^2\)/s).
- \( v \) is the velocity (451 m/s).
Substituting the values and solving for \( m \) will give you the maximum mass.
**Conclusion**
By understanding the principles of de Broglie wavelengths, learners can explore the quantum nature of particles in chemistry. This exercise demonstrates the application of quantum mechanics in predicting the behavior of particles at microscopic scales.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38e21668-df36-4535-9b97-aa4a56ba16f0%2F005d0850-efa3-4b55-a2fd-7547c87d090d%2Fq9lt2b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Exploring the de Broglie Wavelength in Chemistry**
**Introduction to de Broglie Wavelengths**
In the study of quantum mechanics within chemistry, we often encounter the concept of the de Broglie wavelength, which is used to describe the wave-like behavior of particles.
**Problem Statement**
Consider an experiment where the smallest measurable wavelength is 0.890 femtometers (fm). Our goal is to determine the maximum mass of an object for which the de Broglie wavelength is observable for an object traveling at a speed of 451 meters per second (m/s).
**Calculation**
To find the maximum mass \( m \) (in kilograms) where the de Broglie wavelength is observable, use the de Broglie wavelength formula:
\[ \lambda = \frac{h}{mv} \]
Where:
- \( \lambda \) is the wavelength (0.890 fm or \( 0.890 \times 10^{-15} \) meters).
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \) kg m\(^2\)/s).
- \( v \) is the velocity (451 m/s).
Substituting the values and solving for \( m \) will give you the maximum mass.
**Conclusion**
By understanding the principles of de Broglie wavelengths, learners can explore the quantum nature of particles in chemistry. This exercise demonstrates the application of quantum mechanics in predicting the behavior of particles at microscopic scales.
Expert Solution
Step 1
We have been given wavelength of light and velocity of an object.We have been asked to find out mass of an object. Wavelength can be defined as distance between two crests or two troughs.
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