"An element with molar mass 2.7 $\times$ 10-2 kg mol-1 forms a cubic unit cell with edge length 405 pm. If its density is 2.7 $\times$ 103 kg m-3, the radius of the element is approximately ______ $\times$ 10-12 m (to the nearest integer)."

Question

Accepted Answer

"Molar mass of an element (M) = 27 gm mol^–1

Edge length of a cubic unit cell (a) = 405 pm = 4.05 × 10^–8 cm

density of the element (d) = 2.7 gm/cc

d = ${{Z \times M} \over {{N_A} \times {{\left( a \right)}^3}}}$

$\Rightarrow$ 2.7 = $${{Z \times 27} \over {6 \times {{10}^{23}} \times {{\left( {4.05 \times {{10}^{ - 8}}} \right)}^3}}}$$

$\Rightarrow$ Z = 4

The element has fcc unit cell

$\therefore$ $\sqrt 2$a = 4r

$\Rightarrow$ r = ${{1.414 \times 405} \over 4}$

= 143 pm

= 143 × 10^–12 m"

An element with molar mass 2.7 $\times$ 10^-2 kg mol^-1 forms a cubic unit cell with edge length 405 pm. If its density is 2.7 $\times$ 10³ kg m^-3, the radius of the element is approximately ______ $\times$ 10^-12 m (to the nearest integer).

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An element with molar mass 2.7 $\times$ 10-2 kg mol-1 forms a cubic unit cell with edge length 405 pm. If its density is 2.7 $\times$ 103 kg m-3, the radius of the element is approximately ______ $\times$ 10-12 m (to the nearest integer).

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An element with molar mass 2.7 $\times$ 10^-2 kg mol^-1 forms a cubic unit cell with edge length 405 pm. If its density is 2.7 $\times$ 10³ kg m^-3, the radius of the element is approximately ______ $\times$ 10^-12 m (to the nearest integer).