Answer
The neon atom in the sample occupies $3.6997 \times 10^{-3} dm^{3}$ percent of the total volume. Therefore, we have a huge empty space between atoms in the gaseous state.
Work Step by Step
1. Convert nm into dm:
$1 nm = 11^{-11} dm$
$69nm = 6.9 \times 10^{-10} dm$
2. Calculate the volume of the one neon atom:
$V_{a} = \frac{4 \times r^{3} \times π}{3} = \frac{4 \times (6.9 \times 10^{-10} dm)^{3} \times 3.14}{3} = 1.37536 \times 10^{-37} dm^{3}$
3. Muliply the volume of the one atom by the number of the atoms in the sample to get the total volume:
$V_{Ne} = V_{a} \times N= 1.37536 \times 10^{-37} dm^{3} \times 2.69 \times 10^{22} = 3.6997 \times 10^{-5} dm^{3}$
4. Divide the total volume of the neon atom by the total volume of the sample:
$\frac{3.6997 \times 10^{-5} dm^{3}}{1 dm^{3}} = 3.6997 \times 10^{-5}$
