Question

A beam of electrons moving with a speed of 0.01c are used in a two-slit experiment with a slit width of 0.056 mm and a slit separation of 0.168 mm. a) What is the angular width (in rad) of the central diffraction maximum? [3] b) Sketch the intensity pattern (I vs sinθ) from the m=-2 to the m=2 diffraction “dark” spots. Label the sinθ axis at each interference peak (with the correct value for sinθ, do not just write “m=1”). [5] c) What would happen to the pattern produced by the slits if the electrons were slowed down? [1] d) What would happen to the pattern produced by the slits if hydrogen ions (one proton and one neutron) were used instead of electrons? [1]

Answer 1

U=0.010 wildlh of new=a=0.056 mm AW reperation, d= 0.168mm. (a) angulas width, 20 = 24) we know that de Broglie relation = 9x h moa dah mu = 2x6.625x1556 C=3x108 mit 9.1xcotx 0.01x3x10x 0.058 xyos 20=866.698108 rad m=9x103 kg m=+2 (6) m=t1 for mal Wh mco lino=433.3x10 rad -m=-1 for m=2 aline= M₂ d = 2x dinol = 21 ms-2 Aino'=866.678108 red (C) if elecbons are allowed down, us, then A1 (wavelengler amu'aled with eledbon) increase tol heet widin of diffrachon bands increases (spreads) (d) if we Theis velocities are len and masses are more and hence replace elections by hydrogenions (18 & in her here. no clarity of velocily, still massee are more and hence lengen decreases so diffraction bands think (narrowed). wewe