Question

A metal is evaporated in vacuum from a hot filament. The resultant metal atoms are incident upon a quartz plate some distance away and form there a thin metallic film. This quartz plate is maintained at a low temperature so that any metal atom incident upon it sticks at its place of impact without further migration. The metal atoms can be assumed equally likely to impinge upon any element of area of the plate.

If one considers an element of substrate area of size b^2 (where b is the atom diameter), show that the number of metal atoms piled up on this area should be distributed approximately according to a Poisson distribution. Suppose that one evaporates enough metal to form a film of mean thickness corresponding to 6 atomic layers. What fraction of the substrate area is then not covered by metal at all? What fraction is covered, respectively, by metal layers 3 atoms thick and 6 atoms thick?

Answer 1