Question

X-ray analysis Mn–Sialloy with 75% by atoms of Mn and 25% by atoms of Si, showed that the unit cell is cubic and lattice parameter is 2.86 Å. The density of alloy = 6850 kg/m3. How many number of atoms are present in the unit cell ?

Mn : 55 and Si : 28

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

Answer: (A)

2

Answer 2

Let total no. of atoms present in the unit cell = n

\ no. of Mn atoms = $\frac{3}{4}$n ; no. of Si atoms = $\frac{n}{4}$

\ $\frac{\left( \frac{3}{4}n \times 55 + \frac{n}{4} \times 28 \right)}{6 \times 10^{23} \times (2.86)^{3} \times 10^{- 24}}$ = 6.85

or $\frac{n\lbrack 41.25 + 7\rbrack}{6 \times 23.39 \times 0.1}$= 6.85

or n = $\frac{6.85 \times 6 \times 2.339}{48.25}$ = 1.99 ~ 2