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Welcome to our Physics lesson on De Broglie Wave is a Probability Wave, this is the second lesson of our suite of physics lessons covering the topic of De Broglie Wave, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
The phenomena of interference and diffraction of electrons are well explained and interpreted through probability pictures, similar to the method used to figure out photons. Given this, we can assert that: "De Broglie wave for electrons (as well as for other matter particles) is a probability wave." This means that in places of the fluorescent screen where the maxima (bright regions) produced by interference or diffraction do appear, the intensity of De Broglie's wave has the highest intensity while in the positions where there are minima, this intensity is almost zero. In this way, the intensity I of this wave as well as the square of its amplitude a, represent the probability for the electron to strike a specific point of the screen. In other words, it is not taken for granted that an electron will hit a specific point of the screen; everything is just probability (chance for an event to occur).
Summarizing what said above, we can write:
An electron and a photon have an energy of 1eV each. Compare their De Broglie wavelength. Take the mass of photon as 9.1 × 10-31 kg.
Clues:
Eph = Ee = 1 eV = 1.6 × 10-19 J
me = 9.1 × 10-31 kg
(c = 3 × 108 m/s)
(h = 6.626 × 10-34 J · s)
λph = ?
λe = ?
The (kinetic) energy of electron is
and its momentum is
So, combining these equation we obtain the known expression
Thus,
Therefore, the De Broglie wave for this electron is
As for the photon, we have:
Thus, the wavelength of the 1 eV photon is
As you see, the wavelength of photon is about 1000 times greater than De Broglie wavelength of an electron with the same energy. That's why we often consider only the energy and wavelength of photons in most events of quantum physics.
You have reached the end of Physics lesson 19.4.2 De Broglie Wave is a Probability Wave. There are 2 lessons in this physics tutorial covering De Broglie Wave, you can access all the lessons from this tutorial below.
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