A beam of electrons strikes a barrier with two narrow but equal-width slits. A screen is located beyond the barrier. And electrons are detected as they strike the screen. The "center" of the screen is the point equidistant from the slits. When either slit alone is open, electrons arrive per second in a very small region at the center of the screen. When both slits are open, how many electrons will arrive per second in the same region at the center of the screen?
The number of electrons when both slits are open .
Number of electrons when one slit is open
To find the number of electrons when both slits are open
The following relationship can be used to describe the probability of detecting a particle in a given region.
The number of electrons that can be found in the region every second equals the probability of discovering a particle.
When there is only one slit open, useequation (1), such that
When two slits are opened at the same time, the amplitude doubles, assuming they are the same size. Therefore, using equation (2), we can write
Therefore, using the equations (2) and (3), we get,
Therefore when the two slits are open condition.
A brag diffraction experiment is conducted using a beam of electrons accelerated through a potential difference. (a) If the spacing between atomic planes in the crystal is , at what angles with respect to the planes will diffraction maximum be observed? (b) If a beam of -rays products diffraction maxima at the same angles as the electron beam, what is the -ray photon energy?
Classically and nonrelativistically, we say that the energy of a massive free particle is just its kinetic energy. (a) With this assumption, show that the classical particle velocity is . (b) Show that this velocity and that of the matter wave differ by a factor of 2. (c) In reality, a massive object also has internal energy, no matter how slowly it moves, and its total energy is , where . Show that is and that is Is there anything wrong with it ? (The issue is discussed further in Chapter 6.)
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