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You may work with your classmates to arrive at the answer to this problem, but the final submission should be your own work. It is possible to synthesize a wide variety of materials with dimensions in the nanometer range. The transmission electron microscope (TEM) image shows gold nanoparticles (bright white) that have been coated with silica ( SiO2-not as bright). The scale bar in the lower right of the image corresponds to 40.0nm. Assume that the gold nanoparticles are spherical and have a diameter of 15.0nm. Answer the following questions. 1. What is the volume of a single Au particle. 2. What is the mass of the particle (look up the density for gold). 3. If the initial solution that was used to synthesize the gold particles contained 50.0mL of 1.00% (w/vol) Au, how many particles can you synthesize? 4. If the diameter decreases by 10%, what % change will occur in the number of particles made