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The Solid State

Question
CBSEENCH12005584

Potassium crystallises in a simple cubic unit cell. It has an atomic mass of 209 and its density is 91.5 g m–3. What is the edge length of its unit cell? 

Solution

we have given,
Mass= 209 g
Number of  atom per unit cell =1 (Simple cubic)
density =91.5 g m-3
NA =6.023 x1023
edge length of unit cell =?
 
By applying formula


density = Mass x Number of atom per unit cellvolume of unit cell  x avogadro's numberd= M x Za3 x NA91.5 = 209 x 1a3 x 6.023 x 1023a3 =209 x 191.5 x 6.023 x 1023

a= 15.59 x10-8 cm