Answer to Question #108136 in Classical Mechanics for Khadija

Question

How much of you is not vacuum? Outside of the nucleus, an atom contains mostly empty space. Estimate the fraction of the volume of an atom that is occupied by the nucleus. Assume that a typical atom has a linear dimension of about 0.1 nm and that a typical nuclear dimension is about 1 fm. (Note that this problem introduces some new prefixes: n is nano or 10^{-9}10
−9
, p is pico or 10^{-12}10
−12
, f is femto or 10^{-15}10
−15
).

Give your answer as a power of ten. For example, enter: 10^18, or 10^-3 (for 10^{18}10
18
or 10^{-3}10
−3
).

Answer 1

$$\frac{V_n}{V_a}=\frac{a_n^3}{a_a^3}$$

$$\frac{V_n}{V_a}=\frac{(10^{-15})^3}{(0.1\cdot10^{-9})^3}=10^{-15}$$