# If an atom was scaled up to the size of a sports oval with a diameter of 150m ?

1. Feb 3, 2012

### AHUGEMUSHROOM

How big would the nucleus be?
A grain of sand (0.1cm diameter)
A marble (1cm diameter)

It's a grain of sand right(?); since the relationship between the diameter of an atom and its nucleus is 100,000 to 1. 150/0.001= 150,000

2. Feb 3, 2012

### vb2341

Well, that depends on the element you're looking at. Different elements have different ratios of atomic radius to nuclear radius (as you increase Z, you get different Coulombic forces as you add electrons, not to mention you add electron shells). I don't know the mathematical formula(s) to find atomic radii, as I assume they're fairly complex, my best advice would be to look them up on some table. Nuclear radius goes something like A^(1/3)*r, where A is the mass number (number of protons and neutrons) and r = 1.2*10^(-15)m (the radius of a proton/neutron I believe). This is just derived from the volume and radius relation of a sphere, so this probably doesn't hold as well for smaller values of A (as the nucleus isn't quite so spherical I would think, except for A=1, hydrogen, with no neutrons, as its nucleus is just a proton), but for larger values it should work decently.

3. Feb 3, 2012

### cepheid

Staff Emeritus
(150 m) / (100,000) = (1.5 x 102 m)/(1.0 x 105) = 1.5 x 10-3 m = 1.5 mm