# How does one calculate the volume of a nucleus and the volume of an atom (in this case hydrogen)?

The hydrogen atom contains 1 proton and 1 electron. The radius of the proton is approximately 1.0 fm (femtometers), and the radius of the hydrogen atom is approximately 53 pm (picometers).

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Do you mean, how do you find the volume from the given radii, or how these radii are obtained? The former is straightforward (see answer below), the latter is a bit more complicated. –  Benji Remez Oct 20 '12 at 22:05

Model them as spheres. The volume of a sphere is $$V = \frac{4}{3}\pi r^3.$$ This should straightforwardly give you the answer.

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What's the old joke? First, assume the sheep is a sphere ... –  McGarnagle Oct 21 '12 at 18:28

The Size of a proton is an extremely difficult calculation, It cannot be done by hand(so far). It requires an in depth understanding of Strong forces(Non-Abelian Gauge theory) and super-computers(See Lattice QCD)

The radius of the Hydrogen atom is relatively straight forward.(See Bohr Radius) On can derive it from old quantum theory thought angular-momentum Quantization.

you will find the derivations here.

http://en.wikipedia.org/wiki/Bohr_model

$$V=\frac{4}{3}\pi r3$$