Density of a unit cell is represented asρ$$=$$ Effective no. of atom (s)× Atomic mass $$/$$ formula mass Volume of a unit cell $$=Z$$⋅M.NA⋅$$a3where$$, mass of unit cell $$=$$ mass of effective no. of $$atom(s)$$ or $$ion(s)M$$ $$=$$ At. $$mass/formula$$ $$massNA=$$ Avogadro's no. ⇒$$6.023$$×$$1023$$α $$=$$ edge length of unit celSilver crystallizes in a fcc lattice and has a density of $$10.6$$ $$g/cm$$°. What is the length of an edge of the unit cell?An element crystallizes in a structure having fcc unit cell of an edge $$200$$ pm. Calculate the density, if $$100$$ g of this element contains $$12$$ × $$1023$$ atoms: The density of KBr is $$2.75$$ $$g/cm-3$$. The length of the edge of the unit cell is $$654$$ pm. To which type of cubic crystal, KBr belongs?

Question

Density of a unit cell is represented asρ$$=$$ Effective no. of atom (s)× Atomic mass $$/$$ formula mass  Volume of a unit cell $$=Z$$⋅M.NA⋅$$a3where$$, mass of unit cell $$=$$ mass of effective no. of $$atom(s)$$ or $$ion(s)M$$ $$=$$ At. $$mass/formula$$ $$massNA=$$ Avogadro's no. ⇒$$6.023$$×$$1023$$α $$=$$ edge length of unit celSilver crystallizes in a fcc lattice and has a density of $$10.6$$ $$g/cm$$°. What is the length of an edge of the unit cell?An element crystallizes in a structure having fcc unit cell of an edge $$200$$ pm. Calculate the density, if $$100$$ g of this element contains $$12$$ × $$1023$$ atoms: The density of KBr is $$2.75$$ $$g/cm-3$$. The length of the edge of the unit cell is $$654$$ pm. To which type of cubic crystal, KBr belongs?

Infinity Learn · Accepted Answer

$$10.6=4$$×$$108a3$$×$$6.023$$×$$1023$$∴$$a=40.7nm$$ Mass of $$12$$×$$1023$$ atoms $$=100gm$$ Mass of $$6.022$$×$$1023$$ atom $$=10012$$×$$1023$$×$$6.023$$×$$1023=50.18$$∴ ρ$$=4$$×$$50.18$$×$$106.023$$×$$1023$$×$$200$$×$$10$$−$$103=41.66g/cm3By$$ hit and Trial : For fcc Z $$=$$ $$4$$ (4$$ pairs of $$KBr) M $$=$$ $$39$$ $$+$$ $$80$$ $$=$$ $$119$$

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