# So much emptiness

#### Ratzinger

Why is there so much empty space in atoms, in solar systems or between galaxies?
Why is mass-energy always so concentrated on all these different scales?

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#### Berislav

Why is there so much empty space in atoms, in solar systems or between galaxies?
Forces.

Why is mass-energy always so concentrated on all these different scales?
I don't understand.

#### rbj

Ratzinger said:
Why is there so much empty space in atoms, in solar systems or between galaxies?
Why is mass-energy always so concentrated on all these different scales?
regarding atoms, particularly the Bohr model (which is not as accurate as the quantum mechanical model of the H atom), is that electron orbitals have to be as large as they are for the electron's (deBroglie) wave function to have an integer number of cycles going around the orbit.

that is just like the resonant frequencies of a circular pipe. only frequencies where, for each time a sound wave or electron's wave goes around the circuit, the wave function is at the same phase (so as not to cancel the wave from other cycles before or after) of the waves for the other trips around the circuit, only waves of those frequencies will survive the out-of-phase "destructive interference". or stated more simply, only waves with wavelengths that are the circumference divided by an integer number, only those waves will have constructive interference. those waves will team up.

the smallest such circumference in the H atom is $2 \pi$ times what is called the Bohr radius $a_0 = \frac{m_P}{m_e \alpha}l_P$ and it's about half an angstrom. it defines the ballpark of how big atoms are.

that doesn't explain why the subatomic particles, the neutrons and protons and electrons etc., are so much smaller than the Bohr radius. that i do not know. we could appeal to the anthropic principle, i s'pose.

r b-j

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#### Claude Bile

Gravity on both counts for scales larger than solar systems.

Claude.

#### ludi_srbin

I read in some book that if one was to put all the electrons, protons and neutrons together a 1 cm^3 would weight about 10 milion tons.

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