If all the empty space of atoms were removed, how big would this earth be?

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SUMMARY

If all the empty space in atoms were removed, the Earth would compress to approximately 500 meters in diameter. This estimation is based on the radius of an iron atom, which is about 1.2 x 10-10 meters, and the radius of its nucleus at 4.6 x 10-15 meters, resulting in a significant factor of 26,000 in radius. Additionally, the black hole radius of the Earth is calculated to be around 1 centimeter. The initial confusion regarding size comparisons, such as a marble or a large stadium, highlights the need for clarity in understanding atomic scales.

PREREQUISITES
  • Understanding of atomic structure and atomic radii
  • Familiarity with concepts of density and compression
  • Basic knowledge of black hole physics
  • Ability to interpret scientific measurements and scales
NEXT STEPS
  • Research atomic structure and the significance of atomic radii
  • Explore the concept of density in relation to black holes
  • Learn about the implications of compressing matter at atomic levels
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Students, educators, and science enthusiasts interested in atomic physics, cosmology, and the fundamental properties of matter will benefit from this discussion.

sskkambad
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Hi everyone, first time poster.
Considering some of the things discussed here, I apologize if my question sounds simplistic.

If this Earth could be compressed so that all the empty space in atoms would disappear how big would this Earth be?
My science teacher once told me that it would be the size of a marble, and I've also heard that it would be the size of a large stadium. I realize it's not an easy thing to estimate but that seems to be quite a difference.

An example of such scales of atoms would be appreciated. (i.e. I've also been told all 6.5 people in this world could be compressed into the size of a kidney bean)

Thanks!
 
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The stadium is closer. An iron atom has a radius of about 1.2 x 10-10 m and an iron nucleus about 4.6 x 10-15 m. So there is a factor of about 26000 in radius, which means the Earth would be about 500 m across.
 
The black hole radius of the Earth is about 1 cm.
 
Thanks for the answer! Come to think of it, I think my science teacher was referring to the black hole density, not the compressed atom density.
 

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