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?

1 Answer
Ernest Z.
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, #"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)

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