A) \[15\times {{10}^{-3}}\]
B) \[64\times {{10}^{-3}}\]
C) \[5\times {{10}^{-3}}\]
D) \[46\times {{10}^{-3}}\]
Correct Answer: A
Solution :
According to Graham's law of diffusion: \[\frac{{{r}_{A}}}{{{r}_{B}}}=\sqrt{\frac{{{M}_{B}}}{{{M}_{A}}}}\] \[{{M}_{A}}=\frac{100}{2}kg/mol\] \[{{M}_{B}}=\frac{64}{2}kg/mol\] and \[{{r}_{A}}=12\times {{10}^{-3}}\] \[{{r}_{B}}=?\] \[\frac{{{r}_{A}}}{{{r}_{B}}}=\sqrt{\frac{{{M}_{B}}}{{{M}_{A}}}}\] \[\therefore \] \[\frac{12\times {{10}^{-3}}}{{{r}_{B}}}=\sqrt{\frac{64/2}{100/2}}\] \[\frac{12\times {{10}^{-3}}}{{{r}_{B}}}=\frac{8}{10}\] \[{{r}_{B}}=\frac{12\times {{10}^{-3}}\times 10}{8}\] \[=15\times {{10}^{-3}}\]
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