Question

In an alloy consisting of 12.8% metal A and 87.2% metal B by weight, the weights of metals A and B are 61.4 g/mol and 125.7 g/mol, respectively, and densities of 4.27 g/cm^3 and 6.35 g/cm^3, respectively. If the edge length of the unit cell of this alloy is 0.395 nm, determine whether the structure of this alloy will have a volume-centered cubic structure or a face-centered cubic structure.

          In an alloy consisting of 12.8% metal A and 87.2% metal B by weight, the weights of metals A and B are 61.4 g/mol and 125.7 g/mol, respectively, and densities of 4.27 g/cm^3 and 6.35 g/cm^3, respectively. If the edge length of the unit cell of this alloy is 0.395 nm, determine whether the structure of this alloy will have a volume-centered cubic structure or a face-centered cubic structure.
        
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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In an alloy consisting of 12.8% metal A and 87.2% metal B by weight, the weights of metals A and B are 61.4 g/mol and 125.7 g/mol, respectively, and densities of 4.27 g/cm^3 and 6.35 g/cm^3, respectively. If the edge length of the unit cell of this alloy is 0.395 nm, determine whether the structure of this alloy will have a volume-centered cubic structure or a face-centered cubic structure.
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Transcript

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00:02 Hi, this is a video based on crystal structure.
00:05 So, crystal structure is the regular repeated arrangement of atoms.
00:11 The most common type of crystal structures are simple cubic, face center and body centered.
00:36 In the first step, we have to calculate the density of the alloy.
00:47 Density of alloy is calculated by the formula.
00:51 Density of alloy is equal to 1 divided by mass fraction of the a divided by density of a plus mass fraction of b divided by density of b.
01:27 On substituting for above equation we have 1 divided by mass fraction of metal a is 12 .5 % divided by density of a is 4 .27 gram per cmq.
01:46 So we have percentage and density of mass fraction of metal b is 87 .5 divided by density of metal b is 6 .35.
01:59 In both the numerators of the denominator we have percentage.
02:06 So it is my whole equation is multiplied by 100.
02:14 Calculating the density of alloy becomes 5 .985 gram per cm cube.
02:29 In the second part, we have to calculate the mass of the alloy.
02:38 The mass of the alloy is even by 1 divided by mass fraction of a divided by atomic weight of a plus mass fraction of b divided by atomic weight of b...
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