An elemental crystal has density of `8570 kg m^(-3)`. The packing efficiency is `0.67`. If the closest distance between neighbouring atoms is `2.86 Å`. The mass of one atom is `(1 amu = 1.66 xx 10^(-27))kg)`

Options

A. 186 amu
B. 93 amu
C. 46.5 amu
D. 43 amu

Explanation

Let volume of unit cell = V
Volume occupied by atoms = 0.68 V , `n((4)/(3)pix^(3))` = 0.68 v
Also, `2r=2.86 Å implies r=1.43 Å`
density `= (nxx("mass in amu")xx1.66xx10^(-27)"kg")/(V) implies 870 = (0.68xxm xx1.66xx10^(-27))/((4)/(3)pi(1.43)^(3)xx10^(-3))implies` m = 93 amu