A2 Correction

A – La maille cubique simple :

rpolonium = 0,168 nm

r = 0,168 nm = 168.10-10 cm donc  a = 2 x r = 336.10-10 cm

Vatomes = 1 x 4/3 x π x (168.10-10)3 = 1,986170168.10-23 cm3

Vmaille = a3 = (336.10-10)3 = 3,7933056.10-23 cm3

C = 1,986170168.10-23 / 3,7933056.10-23 = 1/6 π = 0,5235987756…

 

Mpolonium = 209 g/mol

mmaille = Z x matome  = Z x ( Matome / N )

= 1 x (209 / 6,023.1023) = 3,470031546.10-22 g

rpolonium = 0,168 nm = 168.10-10 cm         donc  a = 2 x r = 336.10-10 cm

Vmaille = a3 = (336.10-10)3 = 3,7933056.10-23 cm3

ρ = 3,470031546.10-22 / 3,7933056.10-23 = 9,147777458 g/cm3

 

B – La maille cubique à faces centrées :

rargent = 0,145 nm

r = 0,145 nm = 145.10-10 cm       

Selon le théorème de Pythagore :

a2 + a2 = (4r)2 ↔ 2a2 = (4r)2 ↔ a2 = (4r)2 / 2 ↔ a = 4r / √2

↔ a = 2√2 r ↔ a = 2√2 x 145.10-10 = 4,101219331.10-8 cm

Vatomes = 1 x 4/3 x π x (145.10-10)3 = 1,277005054.10-23 cm3

Vmaille = a3 = (4,101219331.10-8)3 = 6,898250915.10-23 cm3

C = 1,277005054.10-23 / 6,898250915.10-23 = 0,1851201224

 

Margent = 107,9 g/mol

mmaille = Z x matome  = Z x ( Matome / N )

        = 4 x (107,9 / 6,023.1023) = 7,165864187.10-22 g

rargent = 0,145 nm = 145.10-10 cm          

donc a = 2√2 r ↔ a = 2√2 x 145.10-10 = 4,101219331.10-8 cm

Vmaille = a3 = (4,101219331.10-8)3 = 6,898250915.10-23 cm3

ρ = 7,165864187.10-22 / 6,898250915.10-23 = 10,38794366 g/cm3