An element with molar mass 27 x 102 kg mol1 forms a cubic un

Question

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

DivineJEE · 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

Explanation

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