An element crystallises as face centred cubic lattice with density as $$5.20$$ g $$/$$ $$cm3$$ and edge length of the side of unit cell as $$300$$ pm. The mass of the element which contains $$3.0$$×$$1024$$ cannot be equal to

Question

An element crystallises as face centred cubic lattice with density as $$5.20$$ g $$/$$ $$cm3$$ and edge length of the side of unit cell as $$300$$ pm. The  mass of the element which contains $$3.0$$×$$1024$$ cannot be equal to

Infinity Learn · Accepted Answer

Z $$=$$ $$4$$ in fcc lattice M $$=$$ ?. d $$=$$ $$5.20$$ g $$/$$ $$cm3a$$ $$=$$ $$300$$, pm $$=$$ $$300$$ × $$10-12$$. m $$=$$ $$3$$ × $$10-10$$. m $$=$$ $$3$$ × $$10-6$$ $$cm3$$∴            $$a3=27$$×$$10$$−$$24$$  $$cm3N0=6.02$$×$$1023$$∴          $$M=dN0a3Z=5.20$$ $$g/cm3$$×$$6.02$$×$$1023$$ mol−$$1$$×$$27$$×$$10$$−$$24$$ $$cm34=$$ $$21.13$$ g $$mol-1Thus$$, $$6.02$$×$$1023$$ atmos have $$=$$ $$21.13$$ g∴    $$3.01$$×$$1024$$  atoms have $$=$$ $$21.136.02$$×$$1023$$×$$3.01$$×$$1024$$ $$g=105.65$$ g

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