In the experiment shown in Figure, the effective slit spacing was 6 μm and the distance from the “slits” to the detection screen was 16 cm. The spacing between the center of one bright line and the next (before magnification) was typically 100 nm. From these parameters, determine the wavelength of the electron beam. What voltage was used to accelerate the electrons?

Figure: These images were produced using the beam of an electron microscope. A positively charged wire was placed in the path of the beam, causing the electrons to bend around either side and interfere as if they had passed through a double slit. The current in the electron beam increases from one image to the next, showing that lhe interference pattern is built up from the statistically distributed light flashes of individual electrons. From P. G. Merli, G. F. Missiroli, and G. Pozzi, American Journal of Physics 44, 306 (1976).

Then from the wavelength of the electron beam, we can calculate the momentum of the electrons and from the momentum of the electron we can calculate the voltage required to accelerate the electron.

Step 2<p>The fringe spacing in Young's double slit experiment is given by(1)

Here, is the fringe separation, is the distance from the slit to screen, is the wavelength and is the slit separation. Hence we have

and

Hence the wavelength is

Hence the wavelength of the electron is 3.75 pm.