An initially uncharged sphere is on an insulated stand and isolated in a chamber. The charge on the sphere is monitored as a beam of monochromatic light shines on the sphere. Initially, nothing happens. The wavelength of the light is slowly decreased. When the wavelength reaches a certain value, a positive charge is suddenly measured on the sphere. The wavelength is then held constant, and the charge continues to increase at a constant rate. The intensity of the beam is then increased without the wavelength being changed, and the rate of increase of the charge becomes greater. (a) In a coherent paragraph-length response, describe the cause of the charge on the sphere and the changes in the observations about the charge, in terms of physics principles.
(b) An electron in the chamber is moving with speed 2×10^5m/s when it collides with a positron (a particle identical to an electron except for the sign of its charge) moving with the same speed in the opposite direction. The particles annihilate each other. How much energy is released due to the annihilation?
(c) In another experiment, a beam of electrons with uniform wavelength λe is incident on a slit, where the width of the slit is much larger than λe. A detector is placed near the slit, but no diffraction pattern is observed. What change should be made that would result in a diffraction pattern? Indicate why this change is the one needed.