If the total volume of a simple cubic unit cell is 6.817×10-23 cm3 what is the volume occupied by particles in unit cell
Answers
Answer:
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Given info : The total volume of a simple cubic unit cell is 6.817 × 10¯²³ cm³.
To find : the volume occupied by particles in unit cell is...
solution : in a simple cubic unit cell,
edge length of unit cell = 2 × radius of each particle.
⇒a = 2r
⇒r = (a/2)
now volume of unit cell = a³ = 6.817 × 10¯²³ cm³ ....(1)
so volume occupied by particles in unit cell = no of particles in unit cell × volume of each particle
= (8 × 1/8) × 4/3 πr³
[ particles are located at corner of a simple unit cell, but each corner is shared by eight unit cell so sharing of particle for each unit cell is 1/8 and also there are eight corner in a cube so total particles = 8 × 1/8]
= 4/3 π (a/2)³
= πa³/6
= (3.14 × 6.817 × 10¯²³)/6 [ from eq (1) ]
= 3.57 × 10¯²³
Therefore volume occupied by particles in the unit cell is 3.57 × 10¯²³ cm³