The six factor formula also includes non-leakage probabilities. consider a point source at the center of a homogeneous sphere of material surrounded by vacuum. what radius is required to stop 90% of the emitted particles from escaping the sphere? answer this question by performing many trials (at least 10,000) with a sphere of radius r [em] using the following algorithm. determine the direction of travel using a uniform sample p e [0, n] (altitude, or top-to-bottom) and 0 [0,2] (azimuth) determine the path length to interaction if interaction occurs outside the sphere, increment the leakage tally and start a new particle. once the particle enters vacuum, it will never scatter back in if the interaction occurs inside the sphere, determine the type of interaction if absorption occurs, increment the absorption tally and start a new particle if scatter occurs, determine the new direction of flight and continue iterating a) what thickness (radius) is needed to stop (absorb) 90% of all thermal neutrons if the sphere is composed of water, with es(thermal) = 3.45 cm-1 and ea(thermal) = 0.022 cm1 try different values of radius r and run no less than 10,000 trials to determine the shielding behavior of a given thickness b) what thickness (radius) is needed to stop (absorb) 90% of all fast neutrons if the sphere is composed of water, with esfast) = 0.97 cm~1 and ea(fast) = 0.012 cm1? try different values of radius r and run no less than 10,000 trials to determine the shielding behavior of a given thickness determine each radius value (part a & b) to no less than 0.1 cm. you wil need to try various values of radius r in order to determine the size of the sphere needed to absorb 90% of the neutrons.