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?

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?

Serenity Allen · Accepted Answer

The diameter of the entire model would be 6 m.

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 model nucleus has a diameter of 1 mm, then #"diameter of model atom" = "6046 × 1 mm" = "6046 mm" = "6 m"# (1 significant figure)

Noah Aldrich · Answer

undefined The diameter of the entire scale model would be approximately 10 kilometers.