1.The density of solid Fe is 7.87 g/cm3. What volume per atom of Fe?

2.As a solid Fe adopts a body centered cubic unit cell. What is the volume of a unit cell of this metal?

3.What is the edge length of a unit cell of Fe?

volume = mass/density give you the macro measurement. Divide by 6.022E23 to arrive at the volume of 1 atom Fe.

2. multiply by 2 to obtain the volume of a unit cell.

3. Extract the cube root of #2 to get a.

1. Ah, Fe! The element that's got solid density and an iron will. Now, the density of solid Fe is 7.87 g/cm3. So, to find the volume per atom of Fe, you'll need to channel your inner mathematician and do some calculations. Divide that density by the molar mass of Fe (55.8 g/mol) and boom - you've got the volume per atom. Just be sure to wear your math hat while doing this!

2. Picture this: a solid chunk of Fe, all nice and clumped together in a body-centered cubic unit cell. It's like a metal fortress! Now, to find the volume of a unit cell, you need to become a mini-architect. Multiply the edge length of the unit cell cubed (since it's a cube) by some mathematical magic, and voila - you've got the volume of that metallic box.

3. Oh, the edge length of a unit cell of Fe - the hidden secret of metal! To uncover it, you'll need to do some sleuthing. Remember, Fe adopts a body-centered cubic unit cell. So, grab your Sherlock Holmes magnifying glass and dive into the mystery. There's a mathematical equation waiting for you, involving the radius of an atom and the edge length. Put your detective skills to use and solve for that edge length! Good luck, my dear Watson!

To answer these questions, we need to use some basic concepts from solid-state chemistry and crystallography.

1. The volume per atom of a substance can be calculated using the formula:

Volume per atom = (Density of solid) / (Number of atoms in one mole of the substance) * (Molar mass)

For solid Fe, the molar mass is 55.845 g/mol. The density of Fe is given as 7.87 g/cm^3. We need to convert this into g/m^3 by multiplying by 1000.

Density of Fe = 7.87 g/cm^3 * 1000 g/m^3 = 7870 g/m^3

The number of atoms in one mole of Fe is given by Avogadro's number as 6.022 * 10^23 atoms/mol.

Now we can calculate the volume per atom of Fe:

Volume per atom = (7870 g/m^3) / (6.022 * 10^23 atoms/mol) * (55.845 g/mol)

= 7.098 * 10^-29 m^3/atom

2. The body-centered cubic (bcc) unit cell has one atom at each of the eight corners and one atom at the center of the cube. The volume of a unit cell can be calculated using the formula:

Volume of unit cell = (Edge length)^3 * (1 atom per unit cell)

Substituting the given values for Fe, since it adopts a bcc unit cell, we need to find the edge length of the unit cell.

3. The edge length of the unit cell can be calculated using the formula:

Edge length = ((4 * Molar mass) / (Density * √3))^1/3

Substituting the given values for Fe:

Edge length = ((4 * 55.845 g/mol) / (7870 g/m^2 * √3))^1/3

= 0.286 nm

Therefore, the edge length of a unit cell of Fe is 0.286 nm.

To find the answers to these questions, we will use the concept of crystallography and atomic packing in solids.

1. The density of solid Fe is given as 7.87 g/cm3. To find the volume per atom of Fe, we need to calculate the atomic volume.

Density is defined as mass per unit volume. In this case, we are given the density (7.87 g/cm3) and we want to find the volume per atom.

To find the volume per atom, we can use the equation:

Density = Mass / Volume

Rearranging the equation to solve for volume:

Volume = Mass / Density

Since we want the volume per atom, we need to convert the mass to the mass per atom. The molar mass of Fe is 55.845 g/mol, which means that one mole of Fe has a mass of 55.845 grams.

Now, we can calculate the volume per atom:

Volume per atom = (Mass per atom / Density)

To find the mass per atom, we divide the molar mass by Avogadro's number (6.022 x 10^23):

Mass per atom = Molar mass of Fe / Avogadro's number

Substituting the values into the equation:

Volume per atom = (Molar mass of Fe / Avogadro's number) / Density

2. As a solid, Fe adopts a body-centered cubic (BCC) unit cell. To find the volume of a unit cell, we need to know the edge length of the unit cell.

In a BCC unit cell, there are two atoms at each corner and one atom at the center of the unit cell. The coordination number, which refers to the number of atoms surrounding a central atom, is 8 for the corner atoms and 1 for the center atom.

The volume of a BCC unit cell can be calculated using the edge length by the equation:

Volume of a BCC unit cell = (Edge length)^3

Now, we need to find the edge length of the unit cell.

The edge length of a BCC unit cell can be determined using the atomic radius of the atom and some simple geometry. For a BCC unit cell, the edge length (a) is related to the atomic radius (r) by the equation:

Edge length (a) = 4 * Radius (r) / sqrt(3)

Once we have the edge length, we can find the volume of the unit cell using the equation mentioned earlier.

3. To find the edge length of a unit cell of Fe, we can use the same formula mentioned above:

Edge length (a) = 4 * Radius (r) / sqrt(3)

The atomic radius of Fe can vary depending on the reference used. However, for simplicity, the atomic radius of Fe can be approximated as 0.124 nm.

Substituting the values into the equation, we can calculate the edge length.