6.5 De Broglie’s Matter Waves

Wavelength assigned to a particle as Planck's constant over momentum, standing-wave orbits explaining quantized angular momentum, and electron diffraction.

University Physics Volume 3, 6.5 De Broglie’s Matter Waves

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12 exercises

6.5 Exercise 1

What is de Broglie’s wavelength of a nonrelativistic proton with a kinetic energy of 1.0 eV?

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6.5 Exercise 2

Find the de Broglie wavelength of an electron in the third excited state of hydrogen.

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6.5 Exercise 3

Find the de Broglie wavelength and kinetic energy of a free electron that travels at a speed of 0.75c.

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6.5 Exercise 4

Which type of radiation is most suitable for the observation of diffraction patterns on crystalline solids; radio waves, visible light, or X-rays? Explain.

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6.5 Exercise 6

If an electron and a proton are traveling at the same speed, which one has the shorter de Broglie wavelength?

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6.5 Exercise 8

Why is the wave-like nature of matter not observed every day for macroscopic objects?

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6.5 Exercise 10

Why does the setup of Davisson–Germer experiment need to be enclosed in a vacuum chamber? Discuss what result you expect when the chamber is not evacuated.

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6.5 Exercise 12

What is the de Broglie wavelength of an electron travelling at a speed of $5.0 \times 10^{6} \text{m}/\text{s}$ ?

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6.5 Exercise 14

What is the de Broglie wavelength of a proton whose kinetic energy is 2.0 MeV? 10.0 MeV?

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6.5 Exercise 16

(a) What is the energy of an electron whose de Broglie wavelength is that of a photon of yellow light with wavelength 590 nm? (b) What is the de Broglie wavelength of an electron whose energy is that of the photon of yellow light?

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6.5 Exercise 18

What is the wavelength of an electron that is moving at a 3% of the speed of light?

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6.5 Exercise 20

What is the velocity of a 0.400-kg billiard ball if its wavelength is 7.50 fm?

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