Question

How many moles of atoms are present on the surface of 2cm long iron rod assuming a cubic shape having FCC unit cell edge length 0.556nm?

• A. $2.57\times {10}^{-8}$
• B. $6.23\times {10}^{-7}$
• C. $4\times {10}^6$
• D. $2.24\times {10}^{-2}$

Answer 1

The correct option is A $2.57\times {10}^{-8}$

$Areaofonefaceofrod={\ell }^2$

$surfaceareaofcubicshaperod=6{\ell }^2$

$areaofonefaceofaunitcell=(0.556\times {10}^{-7}{)}^{2}c{m}^2$

$\therefore Numberofunitcellonsurfaceofrod=\frac{6{\ell }^2}{(0.556\times {10}^{-7}{)}^2}$

$\ell =2cm$

number of moles of atoms

$=\frac{6{\ell }^2\times no.ofatomsononefaceoftheunitcell}{(0.556\times {10}^{-7}{)}^2\times N_A}=\frac{(6\times 4\times 2)}{310.54}=2.57\times {10}^{-8}$