a. The diffusion coefficient of the protein lysozyme (MW = 14.1 kg/mol) is 0.104 × 10⁻⁵ cm² s⁻¹. How long will it take this protein to diffuse an rms distance of 1μm? Model the diffusion as a three-dimensional process.

b. You are about to perform a microscopy experiment in which you will monitor the fluorescence from a single lysozyme molecule. The spatial resolution of the microscope is1 μm. You intend to monitor the diffusion using a camera that is capable of one image every 60 s. Is the imaging rate of the camera sufficient to detect the diffusion of a single lysozyme protein over a length of 1μm?

c. Assume that in the microscopy experiment of part (b) you use a thin layer of water such that diffusion is constrained to two dimensions. How long will it take a protein to diffuse an rms distance of 1μm under these conditions?