# 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?

May 19, 2016

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, $\text{diameter of atom = 6046 × diameter of nucleus}$.

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

$\text{diameter of model atom" = "6046 × 1 mm" = "6046 mm" = "6 m}$ (1 significant figure)