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Ch.7 - Quantum-Mechanical Model of the Atom
All textbooksTro 4th EditionCh.7 - Quantum-Mechanical Model of the AtomProblem 51
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Chapter 7, Problem 51

What is the de Broglie wavelength of an electron traveling at 1.35 x 10^5 m/s?

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1
Identify the formula for the de Broglie wavelength: \( \lambda = \frac{h}{mv} \), where \( \lambda \) is the wavelength, \( h \) is Planck's constant (6.626 x 10^{-34} \text{ m}^2 \text{ kg/s}), \( m \) is the mass of the electron (9.109 x 10^{-31} \text{ kg}), and \( v \) is the velocity of the electron.
Substitute the given velocity \( v = 1.35 \times 10^5 \text{ m/s} \) into the formula.
Substitute the known values for Planck's constant \( h = 6.626 \times 10^{-34} \text{ m}^2 \text{ kg/s} \) and the mass of the electron \( m = 9.109 \times 10^{-31} \text{ kg} \) into the formula.
Calculate the de Broglie wavelength by performing the division \( \lambda = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 1.35 \times 10^5} \).
Simplify the expression to find the de Broglie wavelength \( \lambda \).
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Related Practice
Open Question
What happens to the interference pattern if we attempt to determine which slit the electron passes through using a laser placed directly behind the slits? Additionally, what happens to the interference pattern described in Problem 47 if the rate of electrons passing through the slits is reduced to one electron per hour?
Textbook Question

The resolution limit of a microscope is roughly equal to the wavelength of light used in producing the image. Electron microscopes use an electron beam (in place of photons) to produce much higher resolution images, about 0.20 nm in modern instruments. Assuming that the resolution of an electron microscope is equal to the de Broglie wavelength of the electrons used, to what speed must the electrons be accelerated to obtain a resolution of 0.20 nm?

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Textbook Question

The smallest atoms can themselves exhibit quantum-mechanical behavior. Calculate the de Broglie wavelength (in pm) of a hydrogen atom traveling at 475 m/s.

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Textbook Question

A proton in a linear accelerator has a de Broglie wavelength of 122 pm. What is the speed of the proton?

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Textbook Question

Calculate the de Broglie wavelength of a 143-g baseball traveling at 95 mph. Why is the wave nature of matter not important for a baseball?

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Textbook Question

A 0.22-caliber handgun fires a 1.9-g bullet at a velocity of 765 m/s. Calculate the de Broglie wavelength of the bullet. Is the wave nature of matter significant for bullets?

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