where is the mean free path, is the number of target particles per unit volume, and is the effective fission cross section area. peierls did not perform the calculation, leaving this task to frisch. the chemistry of uranium was not well known at the time, and frisch believed that its density was ; the true value is more like . the fission cross section value was more problematic. for this, frisch turned to a 1939 "nature" article by l. a. goldstein, a. rogozinski and r. j. walen at the radium institute in paris, who gave a value of . this was too large by an order of magnitude; a modern value is about . using the values he had, frisch calculated the value of the mean free path for uranium-235 using avogadro's constant: