Question

A beam of electrons with kinetic energy k1 is incident on a single slit of width a. after passing through the slit, the beam strikes a screen where it is made visible. at the center of the screen directly in front of the slit, the intensity of the pattern on the screen is i1. if the kinetic energy of the beam is increased (keeping the slit width and the number of electrons per second constant), does the intensity of the pattern at the center of the screen increase, decrease, or remain the same? explain your answer.

Answer 1

Increasing the kinetic energy of the electron beam will result in a shorter wavelength, leading to a narrower central diffraction peak in the pattern, but the peak intensity at the screen's center will not necessarily change.

Step-by-step explanation:

When discussing the effect of increasing the kinetic energy of an electron beam on the intensity of the pattern at the center of the screen in a single-slit diffraction experiment, we must consider the nature of the electron's behavior. According to quantum mechanics, electrons have wave-like properties and can form an interference pattern similar to light. If the kinetic energy of the electrons is increased while keeping the slit width and the number of electrons per second constant, the intensity at the center of the screen (i1) might initially seem connected to the energy of electrons; however, it is not directly proportional to it. In single-slit diffraction, the central maximum is the result of the constructive interference of the wave aspects of electrons. An increase in kinetic energy means the electrons have a shorter wavelength, leading to a narrower central diffraction peak, but not necessarily a change in the peak intensity.