2. A computer simulation of diffusion is performed on a square lattice of screen pixels with a spacing of a=0.5 mm. The computer performs the calculations so that the particle jumps at a constant rate of T=1000s-!. The simulation cell is a square of edge length 5cm containing 10,000 pixels. There is just one particle in the simulation cell. It moves by nearest-neighbor jumps, and it remains within the cell. a. Estimate the diffusion coefficient of the particle in this simulation if it moves by a random walk, without the need of vacancies to mediate the jump. b. We change the particle to a trace particle and its jump requires vacancies to mediate, in a correlated walk manner. Vacancies with the concentration of 10-4 are introduced in the cell at random locations. Estimate the value of the trace particle diffusion coefficient in this circumstance. c. Estimate the average time for the tracer particle to jump from the center of the cell to one cell border. d. If we draw a circle having its center at the center of the cell, and the radius of the circle is 2 cm, then estimate the average time for the tracer particle to jump from the center of the circle to the circle border. 2. A computer simulation of diffusion is performed on a square lattice of screen pixels with a spacing of a=0.5 mm. The computer performs the calculations so that the particle jumps at a constant rate of T=1000s-!. The simulation cell is a square of edge length 5cm containing 10,000 pixels. There is just one particle in the simulation cell. It moves by nearest-neighbor jumps, and it remains within the cell. a. Estimate the diffusion coefficient of the particle in this simulation if it moves by a random walk, without the need of vacancies to mediate the jump. b. We change the particle to a trace particle and its jump requires vacancies to mediate, in a correlated walk manner. Vacancies with the concentration of 10-4 are introduced in the cell at random locations. Estimate the value of the trace particle diffusion coefficient in this circumstance. c. Estimate the average time for the tracer particle to jump from the center of the cell to one cell border. d. If we draw a circle having its center at the center of the cell, and the radius of the circle is 2 cm, then estimate the average time for the tracer particle to jump from the center of the circle to the circle border