How would i use the uncertainty principle to estimate the diameter of a hydrogen atom?

Question

i'm in desperate need of help with this quantum assignment and this is just the tip of the iceberg. thanks

Answer 1

No need for uncertainty principle.

The hydrogen atom is composed of a very light, negatively charged electron, and a heavy, positively charged proton. The weight of the proton is 1.00758 atomic mass units (about 6.02 x 10^23 protons weigh 1.00758 grams). The electron weighs about 1/1837 of the proton's weight. The diameter of a proton has a fairly definite meaning, and is 1.6 x 10^-13 cm. The diameter of a hydrogen atom in its ground state is around 1 x 10^-8 cm, so the ratio of the diameters is about 1.6 x 10^-5, which makes the ratio of the volumes 4.1 x 10^-15. The volume occupied by the electron is all but a tiny fraction of the volume of the atom, while 99.95% of the atom's mass is in the proton.