Question Video: Understanding the Effect of Velocity on the Intensity Distribution of a Diffracted Electron Beam | Nagwa Question Video: Understanding the Effect of Velocity on the Intensity Distribution of a Diffracted Electron Beam | Nagwa

Question Video: Understanding the Effect of Velocity on the Intensity Distribution of a Diffracted Electron Beam Physics • Third Year of Secondary School

A beam of electrons passes through a crystal. A diffraction pattern of concentric rings is formed on a screen behind the crystal that records the positions of electrons that arrive at it, as shown in the diagram. The intensity of the rings is plotted against the radial distance from the center of the pattern. The resulting intensity distribution is shown three times, each time compared to another intensity distribution that is shown below it. Which of the intensity distributions would result from decreasing the velocity of the electrons in the beam?

03:01

Video Transcript

A beam of electrons passes through a crystal. A diffraction pattern of concentric rings is formed on a screen behind the crystal that records the positions of electrons that arrive at it, as shown in the diagram. The intensity of the rings is plotted against the radial distance from the center of the pattern. The resulting intensity distribution is shown three times, each time compared to another intensity distribution that is shown below it. Which of the intensity distributions would result from decreasing the velocity of the electrons in the beam? (A) III, (B) I, (C) II, (D) none of these distributions.

This question is asking us about electrons which act like waves passing through a crystal lattice that essentially acts as a line of slits in a screen. When waves pass through a slit, they can be diffracted so that when they emerge, they spread out radially with the most diffraction occurring when the width of the aperture is the same or similar to the wavelength of the wave. Because electrons can act like waves, electrons create similar diffraction patterns.

Waves emerging from neighboring slits or a line of slits can interfere, either constructively, creating a greater intensity at points of constructive interference, or destructively, reducing the intensity.

For this question, we want to know what would happen to a diffraction pattern created by electrons passing through a crystal if the velocity of the electrons was reduced. For this, we need to understand how electrons can behave like waves.

Remember that the de Broglie wavelength for a particle can be found using the following equation. 𝜆 is equal to ℎ over 𝑝, where lambda is the wavelength of the electron, ℎ is the Planck constant, and 𝑝 is the momentum of the electron. Now then, if we decrease the velocity of the electron beam, the momentum will decrease as well, since momentum is dependent on velocity. So this means that decreasing the velocity of the electrons will increase the associated wavelength of the electrons.

If we think about how diffraction patterns are affected by the wavelength of the wave, we know that the greater the wavelength of the wave, the greater the distance between the consecutive bright fringes of the diffraction pattern. A greater distance between bright spots means that when we look at the ring patterns head on, we should expect the concentric bright rings to spread out.

If we take a look at the diagrams, we can see that the first graph shows a decrease in intensity, while the second shows the electron intensity more tightly packed together. It’s difficult to spot, but only the third graph shows the intensity of the electrons being more spread out, which indicates that the concentric fringes would be spaced further apart.

So, the answer is graph III, which corresponds to option (A). Lowering the velocity of the electrons would result in a longer associated wavelength of the electrons and a more spread out diffraction pattern.

Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

  • Interactive Sessions
  • Chat & Messaging
  • Realistic Exam Questions

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy