The neutron interference pattern of FIGURE P39.45 was made by shooting neutrons

Question

The neutron interference pattern of FIGURE P39.45 was made by shooting neutrons with a speed of 200 m/s through two slits spaced 0.10 mm apart. What was the energy, in eV. of the neutrons? What was the de Broglie wavelength of the neutrons? The pattern was recorded by using a neutron detector to measure the neutron intensity at different positions. Notice the 100 firm scale on the figure. By making appropriate measurements directly on the figure, determine how far the detector was behind the slits. FIGURE P39.45 46. The electron beam in a cathode-ray tube is accelerated through a potential difference of 250 V. The electrons then pass through a small circular hole and are viewed on the screen. You observe that the central bright spot on the screen is the base of a cone with its apex at the hole. The outer edge of the cone makes a 0.50 degree angle with the original direction of the electron beam. What is the diameter of the hole?

Explanation / Answer

Distance from central maximum to first side maximum = 2/3 * 100 * 10E-6 s = 6.7 * 10E-5 m wavelength = y = h / (m v) y = 6.62 * 10E-34 / (1.67 * 10E-27 * 200) = 2 * 10E-9 m tan theta = sin theta = s / D where D is distance to screen n y = d sin theta for a double slit y = d s / D D = .0001 * 6.7 * 10E-5 / 2 * 10E-9 = 3.4 m

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