Proving the Size of Atoms is Nearly 10^-8cm

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Discussion Overview

The discussion revolves around the question of how to prove that the size of atoms is nearly 10^-8 cm. Participants explore various methods and calculations related to atomic size, including theoretical and practical approaches.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant suggests calculating the expectation value of the radius for the outermost electrons to estimate atomic size.
  • Another participant mentions that for copper, one can calculate the distance between neighboring atoms using its density and atomic mass, which relates to the atomic radius.
  • A different viewpoint is presented, noting that many heavier atoms are significantly larger than 10^-8 cm, and referencing quantum theory of the hydrogen atom as a potential source for understanding atomic size.
  • Further elaboration on copper's density and atomic mass is provided, indicating how to derive the volume per atom through arithmetic calculations.

Areas of Agreement / Disagreement

Participants express differing views on the size of atoms, with some asserting that many heavy atoms exceed the size of 10^-8 cm, while others focus on specific calculations for copper. The discussion remains unresolved regarding a definitive method to prove the atomic size.

Contextual Notes

Some calculations depend on assumptions about atomic structure and density, and there are unresolved steps in the mathematical reasoning presented.

prochatz
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Hello,
Does anyone know how to prove that the size of atoms is nearly 10^-8cm?:rolleyes:
Thank you
 
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I'd calculate the expectation value of r for the outmost electrons. That should give a ballpark estimate.
 
Copper (for instance) is a close-packed metal. From its density and atomic mass you can calculate the distance between the centers of neighboring atoms. This will be nothing but twice the radius of the copper atom.
 
Gokul43201 said:
Copper (for instance) is a close-packed metal. From its density and atomic mass you can calculate the distance between the centers of neighboring atoms. This will be nothing but twice the radius of the copper atom.

I understood what you mean but I still don't know how to calculate it.:rolleyes:
 
prochatz said:
Hello,
Does anyone know how to prove that the size of atoms is nearly 10^-8cm?:rolleyes:
Thank you

First, many atoms, heavy ones, are much bigger than 10-8 cm.

Second. Read any discussion of the quantum theory of the hydrogen atom and you, with perhaps a bit of work, will find your answer,/
Regards,
Reilly Atkinson
 
prochatz said:
I understood what you mean but I still don't know how to calculate it.:rolleyes:

Copper has a density of 8.92 g/cm^3. It has an atomic mass of 63.5, which means that 63.5 g of copper contains 6.02 x 10^23 atoms (one mole). Using these numbers, you can find the volume (cm^3) per atom just by analyzing the units and doing a little arithmetic. Try it! :smile:
 
Your suggestions were really helpfull, thank you all.:smile:
 

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