Question

Iron has a mass of 7.87 g per cubic centimeter of volume, and the mass of an iron atom is 9.27 × 10-26 kg. If you simplify and treat each atom as a cube, (a) what is the average volume (in cubic meters) required for each iron atom and (b) what is the distance (in meters) between the centers of adjacent atoms?

Answer 1

(a) what is the average volume (in cubic meters) required for each iron atom
For this case, the density of Iron would be 7.87g/cm³

V = 9.27 x 10^-26 kg / 7.87g/cm³ ( 1 kg / 1000 g)
V = 1.18 x 10-23 cm³

(b) what is the distance (in meters) between the centers of adjacent atoms?
We assume the atoms as cube, so we use the volume of the cube to calculate the distance of the atoms.

V = 1.18 x 10-23 cm³ = s³
s = 2.28 x 10^-8 cm

Answer 2

Answer:

a) $1.1823\times 10^{-29}m^3$ is the average volume  required for each iron atom.

b) The distance between the centers of adjacent atoms is $2.2781\times 10^{-8} m$.

Explanation:

a) Mass of an iron = 7.84

Volume of iron = $1 cm^3$

Let the x atoms of iron weights 7.84 g and volume of $1 cm^3$.

Mass of an iron atom = $9.27\times 10^{-26} kg=9.27\times 10^{-23} g$

$x\times 9.27\times 10^{-23} g=7.84 g$

$x =8.4573\times 10^{22} atoms$

Volume of x atoms of iron = $1 cm^3$

Volume of an iron atom = v

$x\times v=1 cm^3$

$v=\frac{1 cm^3}{8.4573\times 10^{22} }=1.1823\times 10^{-23}cm^3$

$1 cm^3= 10^{-6} m^3$

$v=1.1823\times 10^{-29}m^3$

$1.1823\times 10^{-29}m^3$ is the average volume  required for each iron atom.

b) Volume of an iron atom = v

Volume of the cube = $s^3$

Length of iron cube -= s

$1.1823\times 10^{-29}m^3=s^3$

$s=2.2781\times 10^{-8} m$

According to question we are treating iron atom as cube. So all the cubic iron atoms will have a same side.

$s=2.2781\times 10^{-8} m$

The distance between the centers of adjacent atoms:

Horizontal distance of the center from the one face of the cubic iron atom:

=$\frac{s}{2}$

Horizontal distance of the center from the one face of the another cubic iron atom:

=$\frac{s}{2}$

$\frac{s}{2}+\frac{s}{2}=s$

The distance between the centers of adjacent atoms is $2.2781\times 10^{-8} m$.