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DedPeter [7]
3 years ago
10

An AX ceramic compound has the rock salt crystal structure. If the radii of the A and X ions are 0.137 and 0.241 nm, respectivel

y, and the respective atomic weights are 22.7 and 91.4 g/mol, what is the density (in g/cm3) of this material?
A. 0.438g/cm3
B. 0. 571g/cm3
C. 1.75g/cm3
D. 3.50g/cm3

Engineering
1 answer:
Tju [1.3M]3 years ago
3 0

Answer:

c) 1.75 g/cm³

Explanation:

Given that

Radii of the A ion, r(c) = 0.137 nm

Radii of the X ion, r(a) = 0.241 nm

Atomic weight of the A ion, A(c) = 22.7 g/mol

Atomic weight of the X ion, A(a) = 91.4 g/mol

Avogadro's number, N = 6.02*10^23 per mol

Solution is attached below

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Answer:

atomic radius  R = 0.157 nm

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Explanation:

given data

parameters a =  0.413 nm

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atomic packing factor = 0.536

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to find out

atomic radius and  atomic weight

solution

we apply  here atomic packing factor (x) that is

atomic packing factor (x) = \frac{volume(sphere)}{volume(unit\ cell)}  ..................1

put here value we get

atomic packing factor = \frac{8*(4/3)*\pi R^3}{3*a*b*c}

R = (\frac{3(x)(abc)}{32\pi })^{1/3}

R =  (\frac{3(0.536)(0.413*0.665*0.876)}{32\pi })^{1/3}

atomic radius  R = 0.157 nm

and

now we get here metal atomic weight that is

metal atomic weight = \frac{\rho (abc)(N_A)}{no\ of\ atom}   ....................2

metal atomic weight = \frac{3.99 (0.413*0.665*0.876)(6.023*10^{23})}{8}  

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