Question

The diameter of an atom is 1.1×10−10m and the diameter of its nucleus is 1.0×10−14m. Part A What percent of the atom's volume is occupied by mass? Express your answer using two significant figures.

Answer 1

To solve this problem we will use the basic concept given by the Volume of a sphere with which the atom approaches. The fraction in percentage terms would be given by the division of the total volume of the nucleus by that of the volume of the atom, that is,

$\% Percent = \frac{V_{nucleus}}{V_{atom}}*100$

$\% Percent = \frac{4/3 \pi (d_{nucleus}/2)^3}{4/3 \pi (d_{atom}/2)^3}*100$

$\% Percent = \frac{(d_{nucleus}/2)^3}{ (d_{atom}/2)^3}*100$

$\% Percent =\frac{(1.0*10^{-14}/2)^3}{ (1.1*10^{-10}/2)^3}*100$

$\% Percent = 7.51*10^{-13}*100$

$\% Percent = 7.51*10^{-11}\%$

Therefore the percent of the atom's volume is occupied by mass is $7.51*10^{-11}\%$