Question

Calculate density of Fe crystal if that crystallises in FCC unit cell with an edge
length of 200 pm. Atomic mass of 'Fe' = 56 g/mol (Assume, Na = 6 * 1023)
(1) 4.66 g/cm3
(2) 46.66 g/cm3
(3) 2.33 g/cm3
(4) 23.33 g/cm3​

Answer 1

Answer:

i dont know! Tell me the answer of this question

Answer 2

Fe crystal crystallises in FCC unit cell with an edge length of 200 pm. Atomic mass of Fe = 56 g/mol.

We have to find the density of Fe crystal.

no of atoms per unit in face centered cubic lattice (FCC) , Z = 4

volume of unit cell, V = a³

where a is edge length of unit cell.

= (200 pm)³

= (2 × 10¯¹⁰)³

= 8 × 10¯³⁰ m³

= 8 × 10¯³⁰ × 10⁶ cm³

= 8 × 10¯²⁴ cm³

Atomic mass of Fe , M = 56 g/mol

Given, Avogadro's number, $N_a$ = 6 × 10²³

we know, the density of a Crystal is given by, $\rho=\frac{ZM}{VN_a}$

= $\frac{4\times56}{8\times10^{-24}\times6\times10^{23}}$

= 46.66 g/cm³

Therefore the density of the Fe crystal is 46.66 g/cm³ . so option (2) is correct correct.