Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see in figure).
In an experiment, electrons are made to pass through a narrow slit of width 'd' comparable to their de Broglie wavelength. They are detected on a screen at a distance 'D' from the slit (see figure).
Which of the following graph can be expected to represent the number of electrons 'N' detected as a function of the detector position 'y' (y=0 corresponds to the middle of the slit)?Electron plane wave incident on a single slit of width d; screen at distance D.
(A)(see structure)
(B)(see structure)
(C)(see structure)
(D)(see structure)✓ Correct
Answer: (D)
Solution
When the slit width is comparable to the electron's de Broglie wavelength the electrons diffract, so the count on the screen is not a sharp geometric shadow but a single-slit diffraction pattern. The number detected is greatest straight ahead at y=0, forming a broad central maximum, and falls away to subsidiary maxima of much smaller height on either side, with minima in between. The graph showing a tall central peak flanked by small side peaks is the one that represents this distribution.
JEE Main · 2008 · 27 Apr 2008 · Offline · Single correct option
