Question

iron - 56 contains 26 protons and 26 electrons. the radius of the nucleus is approximately 4.9 fm (femtometers), and the radius of the iron atom is approximately 156 pm (picometers). part a calculate the volume of the nucleus and the volume of the atom for iron. (hint: convert both given radii to meters first.) express your answers in cubic meters to two significant figures separated by a comma. part b what percentage of the iron atoms volume does the nucleus occupy? express your answer in percent to two significant figures.

Explanation:

Step1: Convert units

• Convert radius of nucleus \(r_{nucleus}=4.9\ fm = 4.9\times10^{-15}\ m\)
• Convert radius of atom \(r_{atom}=156\ pm=156\times 10^{-12}\ m\)

Step2: Calculate volume of sphere

The formula for the volume of a sphere is \(V = \frac{4}{3}\pi r^{3}\)

• For nucleus:

\(V_{nucleus}=\frac{4}{3}\pi r_{nucleus}^{3}=\frac{4}{3}\pi(4.9\times 10^{-15})^{3}\)

$$
LATEXBLOCK0
$$

• For atom:

\(V_{atom}=\frac{4}{3}\pi r_{atom}^{3}=\frac{4}{3}\pi(156\times 10^{-12})^{3}\)

$$
LATEXBLOCK1
$$

Step3: Calculate percentage

The percentage of the atom's volume that the nucleus occupies is \(\frac{V_{nucleus}}{V_{atom}}\times100\%\)

$$
LATEXBLOCK2
$$

Answer:

• Part A: \(V_{nucleus}:V_{atom}=4.9\times 10^{-43},1.6\times 10^{-29}\ m^{3}\)
• Part B: \(\frac{V_{nucleus}}{V_{atom}} = 3.1\times 10^{-12}\%\)