#### Question

# What fraction of a hydrogen atom is occupied by the nucleus?

The nucles of a H atom is a single proton and the radius is approx 1 fm. i found the approx value of the proton which is 4.2E-45 m^3, the Bohr radius is 5e-11 m, and the approx volume of the hydrogen atom is 5.2E-31 m^3.

How do i find the fraction of a hydrogen atom that is occupied by the nuclues?

#### Answer

volume of a sphere is given by:

> V = (4/3)πr3

thus the fractional ratio would be given by:

> V?/V? = [(4/3)πr?3] / [(4/3)πr?3]

but "four-thirds pi" will cancel itself, leaving:

> V?/V? = (r?3)/(r?3)

volume ratio using given radii of the greater and lesser spheres:

> V?/V? = [(1.0 × 10?1? m)3]/[(5.0 × 10?11 m)3]

> V?/V? = (1.0 × 10? m3)/(1.25 × 10?31 m3)

> V?/V? = (8.0 × 10?1?)

> V?/V? = 1 / (1.25 × 101?)

using less rounded figures the ratio is only slightly less disparate:

> V?/V? = [(8.768 × 10?1?)3]/[(5.2917721092 × 10?11 m)3]

> V?/V? = (6.74064761 × 10? m3)/(1.48184711 × 10?31 m3)

> V?/V? = (4.54881449 × 10?1?)

> V?/V? = 1 / (2.19837499 × 101?)

for an introductory physics course anything within the negative-15th order of magnitude should be an acceptable answer.