A critical component in a physics experiment is a 5 mm thick plate of high purit

Question

A critical component in a physics experiment is a 5 mm thick plate of high purity copper plated with a thin layer of silver 50 nm thick. To operate properly, the copper must have less than 100 parts per million silver concentration at a depth of 1 mm from the surface. The plate was accidentally exposed to a high temperature of 1000degreeC for 24 hours, during which time diffusion occurred. You must decide whether a new plate needs to be fabricated, or if the old one is still usable. The silver follows the behavior of a "thin film solution". For Ag in Cu at 1000 degree C, D = 1.0 Times 10-12 m2/sec. Assume that there are about 7.0 Times 1028 atoms/m3 for both Ag and Cu.

Explanation / Answer

The plates was accidentally exposed to high temperature of 1000 0C for 24 hours, during which time diffusion occurred.

using an equation,    t = x2 / 2 D

where, x = depth from the surface = 1 x 10-3 m

D = diffusion coefficient = 1 x 10-12 m2/sec

inserting these values in above eq.

time diffusion occurred is given as, t = (1 x 10-3 m)2 / 2 (1 x 10-12 m2/sec)

t = (10-6 m2) / (2 x 10-12 m2/sec)

t = 0.5 x 106 sec

t = 5 x 105 sec

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