- Consider A Two Slit Interference Pattern Experiment But One Where The Slits Are Atomic With Spacing Created Between Sh 1 (510.13 KiB) Viewed 41 times
Consider a two-slit interference pattern experiment, but one where the slits are atomic with spacing, created between sheets of atoms, with d = 1.70 Å (one Å = angstrom is equivalent to 0.1 nm). A screen is located L = 3.90 m in front of the slits. Parts (a) through (c) involve a beam of high-energy electrons passing through the slits and creating an interference pattern on a screen. The small angle approximation can be used for the interference pattern. р (a) What velocity, v in m/s, must each electron in the beam have in order for the spacing on the screen between adjacent interference maxima to be Ay = 28.1 um? Ignore relativity. (b) Now, correct for relativity. What is the more accurate value of velocity, possessed by each electron in the beam? Note, it is the momentum that determines the de Broglie wavelength, 2 = thus you need to relate electron momentum, p, and relativistic kinetic energy, Kret, using E2 = (mc2)2 + (pc)2 and E = Krel + mc? (c) With nothing else changed, except the kinetic energy per electron in the beam, what would be the interference maxima spacing on the screen if the kinetic energy per electron equaled its rest energy? Do you need to account for relativity here? Parts (d) through (e) involve waves other than electrons passing through the same slits and creating an interference pattern on the same screen. The small angle approximation can be used for the interference pattern. (d) Consider the value of relativistic kinetic energy, Krel, per electron that matches the corrected velocity your found in part (b), and compare that value to how much energy each photon, Ephoton, would have in a beam of gamma rays that created the same interference pattern spacing of Ay 28.1 um on the screen. What is the ratio of the energies Ephoton ? Krel (e) Consider the value of relativistic kinetic energy, Kret, per electron that you found in part (b) and use it to find the correct velocity of each electron. If a beam of neutrons, with a mass of m = 1.67 x 10-27 per neutron were sent through the same atomic slits, what velocity would they need to create the same interference pattern spacing of Ay = 28.1 um on the screen?