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In the experiment shown in Figure, the effective slit
Chapter , Problem 6P(choose chapter or problem)
Problem 6P
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).
Questions & Answers
QUESTION:
Problem 6P
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).
ANSWER:
Step 1
In this problem, the slit spacing, the fringe separation and the distance from the slit to screen is given. We have to use the formula of double slit interference and calculate the wavelength of the electron beam.
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.