A domain in ferromagnetic iron is in the form of a ube of side length `2mum` then the number of iron atoms in the domain are `("Molecular mass of iron"= 55gmol^(-1) and "density"=7.92 g cm^(-3))`

Options

A. `6.92xx10^(12)"atoms"`
B. `6.92xx10^(11)"atoms"`
C. `6.92xx10^(10)"atoms"`
D. `6.92xx10^(13)"atoms"`

Explanation

To find the number of iron atoms in a ferromagnetic domain shaped like a cube with a side length of 2 micrometers, we can follow these steps:

### Step 1: Calculate the Volume of the Cube
The volume \( V \) of a cube is given by the formula:
\[ V = \text{side}^3 \]
Given that the side length is \( 2 \, \mu m = 2 \times 10^{-6} \, m \), we can calculate the volume:
\[ V = (2 \times 10^{-6} \, m)^3 = 8 \times 10^{-18} \, m^3 \]
To convert this volume to cubic centimeters (since \( 1 \, m^3 = 10^6 \, cm^3 \)):
\[ V = 8 \times 10^{-18} \, m^3 = 8 \times 10^{-12} \, cm^3 \]

### Step 2: Calculate the Mass of the Iron in the Domain
Using the density \( \rho \) of iron, which is given as \( 7.92 \, g/cm^3 \), we can find the mass \( m \) using the formula:
\[ m = \rho \times V \]
Substituting the values:
\[ m = 7.92 \, g/cm^3 \times 8 \times 10^{-12} \, cm^3 = 6.336 \times 10^{-11} \, g \]

### Step 3: Calculate the Number of Moles of Iron
To find the number of moles \( n \), we use the molecular mass of iron, which is \( 55 \, g/mol \):
\[ n = \frac{m}{\text{molecular mass}} = \frac{6.336 \times 10^{-11} \, g}{55 \, g/mol} \]
Calculating this gives:
\[ n \approx 1.152 \times 10^{-12} \, mol \]

### Step 4: Calculate the Number of Atoms
Using Avogadro's number \( N_A = 6.023 \times 10^{23} \, atoms/mol \), we can find the total number of atoms \( N \):
\[ N = n \times N_A = 1.152 \times 10^{-12} \, mol \times 6.023 \times 10^{23} \, atoms/mol \]
Calculating this gives:
\[ N \approx 6.92 \times 10^{11} \, atoms \]

### Final Answer
The number of iron atoms in the domain is approximately:
\[ \boxed{6.92 \times 10^{11}} \, \text{atoms} \]