2.6 A seed crystal of diameter D (mm) is placed in a solution of dissolved salt, and

new crystals are observed to nucleate (form) at a constant rate $\displaystyle r (crystals \\\\ min^{-1}) $ .

Experiments with seed crystals of differentt sizes show that the rate of nucleation

varies with the seed crystal diameter as

$\displaystyle r(crystals\\ min^{-1}) = AD + BD^{2} $

where D is in mm, and where A and B are constants (which must be determined).

(a) What are the units of the constants A and B? Suppose that a D = 1 mm

seed crystal produces a nucleation rate of r = 210 crystals min��1, whereas a

D = 2 mm seed crystal produces a nucleation rate of r = 440 crystals min��1.

Use this information to evaluate A and B.

(b) Calculate the crystal nucleation rate in crystals min��1 for a seed crystal di-

ameter of 0.05 inch.

(c) Derive a formula for r (crystals min��1) in terms of D (in). What are the

values and units of the constants in the expression? Check the formula with

the result of 2.6(b). Comment on your results.

(d) Derive a formula for $\displaystyle r (crystals s^{-1}) $ . what are the values snd units of the constants in the expression.