Learning Goal: To understand how to find the wavelength and diffraction patterns

Question

Learning Goal:

To understand how to find the wavelength and diffraction patterns of electrons.

An electron beam is incident on a single slit of width a. The electron beam was generated using a potential difference of magnitude V. After passing through the slit, the diffracted electrons are collected on a screen that is a distance L away from the slit. Assume that V is small enough so that the electrons are nonrelativistic. Ultimately, you will find the width of the central maximum for the diffraction pattern.

Part A

In any diffraction problem, the wavelength of the waves is important. To find the wavelength of electrons, you can use the de Broglie relation =hp, but you first must find the momentum of one of the electrons. The electrons are accelerated through a potential difference V. Use this information to find the momentum p of the electrons.

Express your answer in terms of the mass of an electron me, the magnitude of the charge on an electron e, and V.

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Part B

This question will be shown after you complete previous question(s).

Part C

This question will be shown after you complete previous question(s).

Learning Goal:

To understand how to find the wavelength and diffraction patterns of electrons.

An electron beam is incident on a single slit of width a. The electron beam was generated using a potential difference of magnitude V. After passing through the slit, the diffracted electrons are collected on a screen that is a distance L away from the slit. Assume that V is small enough so that the electrons are nonrelativistic. Ultimately, you will find the width of the central maximum for the diffraction pattern.

Part A

In any diffraction problem, the wavelength of the waves is important. To find the wavelength of electrons, you can use the de Broglie relation =hp, but you first must find the momentum of one of the electrons. The electrons are accelerated through a potential difference V. Use this information to find the momentum p of the electrons.

Express your answer in terms of the mass of an electron me, the magnitude of the charge on an electron e, and V.

SubmitHintsMy AnswersGive UpReview Part

Part B

This question will be shown after you complete previous question(s).

Part C

This question will be shown after you complete previous question(s).

Explanation / Answer

Part A) Potential energy of the electron is converted to its kinetic energy.

KE = PE

=> mv2/2 = eV

=> p2/2me = eV

=> p = (2emeV)1/2

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