Consider a beam of electrons in a vacuum, passing through a very narrow slit of

Question

Consider a beam of electrons in a vacuum, passing through a very narrow slit of width 2.00m. The electrons then head toward an array of detectors a distance 1.076 m away. These detectors indicate a diffraction pattern, with a broad maximum of electron intensity (i.e., the number of electrons received in a certain area over a certain period of time) with minima of electron intensity on either side, spaced 0.501 cm from the center of the pattern. What is the wavelength of one of the electrons in this beam

Explanation / Answer

We know that, deBorglie relationship is:

lambda,l = h/p where lambda= wavelength and p = momentum

We have been given x(min) = L l/a and the values for x(min), L, and a

So we need to solve for l

l = a*x(min)/L = 2*10^(-6)*0.501*10^(-2)/1.076 = 9.31* 10^(-9) m

So, this is the required wavelength.

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