Magnetic moment of an iron atoms is `1.75 xx 10^(-23) A - m^(2)`. If dipole moments of all the atoms of an iron bar of 6 cm `xx` 1 cm `xx` 1 cm are aligend , the dipole moment of the bar will be (Atomic weight of iron is 56 and density is `7.8 g//cm^(3)`.)

Options

A. `7.0 A - m^(2)`
B. `7.8 A - m^(2)`
C. `8.8 A -m^(2)`
D. `9.6 A - m^(2)`

Explanation

To solve the problem, we need to calculate the dipole moment of an iron bar given the magnetic moment of an iron atom, the dimensions of the bar, the atomic weight of iron, and its density. Here’s a step-by-step solution:

### Step 1: Calculate the Volume of the Iron Bar
The dimensions of the iron bar are given as 6 cm x 1 cm x 1 cm. We can calculate the volume (V) using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Substituting the values:
\[ V = 6 \, \text{cm} \times 1 \, \text{cm} \times 1 \, \text{cm} = 6 \, \text{cm}^3 \]

**Hint:** Remember that the volume of a rectangular object is calculated by multiplying its length, width, and height.

### Step 2: Calculate the Mass of the Iron Bar
To find the mass (m) of the iron bar, we can use the formula:
\[ m = \text{density} \times \text{volume} \]
Given that the density of iron is 7.8 g/cm³, we can substitute the values:
\[ m = 7.8 \, \text{g/cm}^3 \times 6 \, \text{cm}^3 = 46.8 \, \text{g} \]

**Hint:** The mass of an object can be calculated by multiplying its density by its volume.

### Step 3: Calculate the Number of Moles of Iron
Next, we need to calculate the number of moles (n) of iron in the bar using the formula:
\[ n = \frac{\text{mass}}{\text{molar mass}} \]
The molar mass of iron is given as 56 g/mol. Substituting the values:
\[ n = \frac{46.8 \, \text{g}}{56 \, \text{g/mol}} = 0.8357 \, \text{mol} \]

**Hint:** The number of moles can be found by dividing the mass of the substance by its molar mass.

### Step 4: Calculate the Number of Atoms
To find the total number of atoms (N) in the iron bar, we can use Avogadro's number (approximately \(6.02 \times 10^{23}\) atoms/mol):
\[ N = n \times N_A \]
Substituting the values:
\[ N = 0.8357 \, \text{mol} \times 6.02 \times 10^{23} \, \text{atoms/mol} \approx 5.03 \times 10^{23} \, \text{atoms} \]

**Hint:** The total number of atoms can be calculated by multiplying the number of moles by Avogadro's number.

### Step 5: Calculate the Total Magnetic Dipole Moment of the Bar
Finally, we can calculate the total magnetic dipole moment (M) of the bar using the formula:
\[ M = \text{magnetic moment of one atom} \times N \]
Given that the magnetic moment of one iron atom is \(1.75 \times 10^{-23} \, \text{A m}^2\), we substitute the values:
\[ M = 1.75 \times 10^{-23} \, \text{A m}^2 \times 5.03 \times 10^{23} \approx 8.81 \, \text{A m}^2 \]

**Hint:** The total magnetic dipole moment is found by multiplying the magnetic moment of a single atom by the total number of atoms.

### Final Answer
The dipole moment of the iron bar is approximately \(8.81 \, \text{A m}^2\).