Question

If you were to make a scale model of the hydrogen atom and decided the nucleus was to have a diameter of 1mm, what would the diameter of the entire model be?

Answer 1

The diameter of the entire model would be 6 m.

Explanation:

The diameter of a proton is `1.75 × 10^"-15" color(white)(l)"m"`.

The Bohr radius — the most probable distance from the nucleus to the electron — is `5.29 × 10^"-11"color(white)(l) "m"`.

The diameter of a hydrogen atom is therefore `2× 5.29 × 10^"-11" color(white)(l)"m" = 1.058 × 10^"-10" color(white)(l)"m"`.

`"diameter of atom"/"diameter of proton" = (1.058 × 10^"-10" color(red)(cancel(color(black)("m"))))/(1.75 × 10^"-15" color(red)(cancel(color(black)("m")))) = 6046`

That is, `"diameter of atom = 6046 × diameter of nucleus"`.

If the diameter of the model nucleus is 1 mm, then

`"diameter of model atom" = "6046 × 1 mm" = "6046 mm" = "6 m"` (1 significant figure)