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

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In summary, the conversation revolves around proving the size of atoms is nearly 10^-8cm. Suggestions are given to calculate the expectation value of r, use the density and atomic mass of copper to find the distance between neighboring atoms, and to read about the quantum theory of the hydrogen atom. Finally, it is suggested to use the density and atomic mass of copper to find the volume per atom and calculate the size of atoms from there. The conversation ends with gratitude for the helpful suggestions.
  • #1
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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  • #2
I'd calculate the expectation value of r for the outmost electrons. That should give a ballpark estimate.
 
  • #3
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.
 
  • #4
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:
 
  • #5
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
 
  • #6
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:
 
  • #7
Your suggestions were really helpfull, thank you all.:smile:
 

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

What is the significance of proving the size of atoms is nearly 10^-8cm?

Proving the size of atoms is nearly 10^-8cm is significant because it helps us understand the fundamental building blocks of matter and how they interact with each other. It also allows us to make accurate predictions and advancements in fields such as chemistry, physics, and materials science.

How is the size of atoms measured?

The size of atoms is measured using techniques such as X-ray crystallography, electron microscopy, and atomic force microscopy. These methods allow us to visualize and measure the dimensions of atoms and their components.

How was it originally determined that the size of atoms is nearly 10^-8cm?

The size of atoms was originally determined by the English scientist Ernest Rutherford in 1911 through his gold foil experiment. He observed that most of the alpha particles passed through the gold foil, indicating that atoms are mostly empty space. Based on the number of particles that were deflected, he was able to calculate the size of the atom to be approximately 10^-8cm.

Is the size of atoms always the same?

No, the size of atoms can vary depending on the element and its atomic structure. Atoms can also change in size under different conditions, such as when they are heated or compressed.

How does knowing the size of atoms impact our daily lives?

Knowing the size of atoms has a significant impact on our daily lives as it has led to advancements in technology, medicine, and industry. It allows us to create new materials, develop more efficient energy sources, and understand the properties of substances we encounter every day.

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