A sample of 5.4 g of aluminium (M=27 g mol^-1, ccp structure) is considered. Using N_A = 6.022x10^23 mol^-1, find the number of tetrahedral voids in the sample, in units of 10^23 (two decimals).

JEE Main levelNumerical answerDifficulty 2 of 3ss016

A sample of $5.4 g$ of aluminium ( $M = 27 g mo l^{- 1}$ , ccp structure) is considered. Using $N_{A} = 6.022 \times 1 0^{23} mo l^{- 1}$ , find the number of tetrahedral voids in the sample, in units of $1 0^{23}$ (two decimals).

Numerical answer type, answer in x 10^23, tolerance 0.02.

Moles of Al

= 5.4/27 = 0.200

, so atoms

= 0.200 \times 6.022 \times 1 0^{23} = 1.2044 \times 1 0^{23}

. A close-packed lattice has 2 tetrahedral voids per atom, so voids

= 2 \times 1.2044 \times 1 0^{23} = 2.41 \times 1 0^{23}