9 9 D d 2 8 optical path difference
1- Firstly, the electrons produced by heating a tungsten filament are accelerated by a potential difference ΔV. Knowing that the electrons are initially at rest, use the principle of conservation of energy to express the final speed of the electrons (v), as a function of their mass (m), their charge (e) and the potential difference (ΔV) to which they are exposed.
2- Using the relationship obtained in step 1, give an expression for the non-relativistic momentum of the electrons.
3- Pose the de Broglie relation which allows us to obtain the wavelength for the electron. Then express this wavelength using the relationship obtained in step 2 and Planck's constant.
4- The accelerated electrons will strike the graphite film (see image). Express the path difference between electrons 1 and 2 as a function of the angle θ and the distance between 2 planes of carbon atoms of graphite film (d).
5- Use the constructive interference condition to obtain a relationship between the path difference (obtained in step 4) and the wavelength of the electron. Use the variable n for the order of interference. You may view reflections as harsh.
6- The diffracted electrons will be observed on a fluorescent screen located at a distance L from the graphite film (see the other image). Obtain a trigonometric relationship that gives the distance D as a function of L and θ. Next, isolate θ and place it in the relation obtained in step 5.
7- You still have to substitute the wavelength of the electron by its expression predicted by de Broglie obtained in step 3. Do not forget to take into account the 2 redicular distances d1 and d2 illustrated in the second image which are responsible for the 2 distances D that you will observe.
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