GATE 2022 MT – Question 56
For $x>0$, solute concentration is $C=a_1x^2+a_2x$ atoms/mm$^3$, where $x$ is in mm and $a_1,a_2$ have units atoms/mm$^5$ and atoms/mm$^4$. Set their numerical values to 1. For diffusivity $3\times10^{-3}$ mm$^2$/s, the flux magnitude at $x=2$ mm is ______ $\times10^{-3}$ atoms mm$^{-2}$ s$^{-1}$ (nearest integer).
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Correct answer: 15 to 15
Explanation
Fick’s law gives $|J|=D|dC/dx|$. The gradient is $2x+1=5$ atoms/mm$^4$ at x = 2 mm.
Thus $|J|=(3\times10^{-3})(5)=15\times10^{-3}$ atoms mm$^{-2}$ s$^{-1}$. Coefficient: **15**.