Copper atoms stack like cannonballs. We can calculate the atom size by assuming the atoms are shaped like either cubes or spheres. For copper atoms,

Density         = D              =       8900 kg/m3
Atomic mass unit= M0             = 1.661⋅10-27 kg
Atomic mass     = MA             =      63.55 Atomic mass units
Mass            = M   =  MA⋅M0    = 9.785⋅10-26 kg
Number density  = N   =  D / M   = 9.096⋅1028  atoms/m3
Cube volume     = Υcube=  1 / N   = 1.099⋅10-29 m3            Volume/atom if the atoms are cubes
Cube length     = L   =  Υ1/3cube = 2.22⋅10-10  m             Side length of the cube
Sphere fraction = f   =  π/(3√2) =     .7405                Fraction of volume occupied by spheres in a stack o spheres
Sphere volume   = Υsph=  Υcube f  = 8.14⋅10-30  m3 = 4⁄3πR3    Volume/atom if the atoms are spheres
Sphere radius   = R              = 1.25⋅10-10  m

Chemistry

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Bohr model of the atom

The "de Broglie wavelength" of a particle is

Particle momentum    =  Q
Planck constant      =  h  =  6.62*10^-34 Joule seconds
Particle wavelength  =  W  =  h/Q             (de Broglie formula)

The Bohr hypothesis states that for an electron orbiting a proton, the number of electron wavelengths is an integer. This sets the characteristic size of a hydrogen atom.

Orbit circumference  =  C  =  N W           where N is a positive integer

  N   Orbital

  1     S
  2     P
  3     D
  4     F

Electron mass      =  m                =  9.11*10-31 kg
Electron velocity  =  V
Electron momentum  =  Q  = m V
Electron charge    =  e                =  -1.60*10-19 Coulombs
Coulomb constant   =  K                =  9.0*109  Newtons meters / Coulombs2
Electric force     =  Fe  =  K e2 / R2
Centripetal force  =  Fc  =  M V2 / R
Orbit radius       =  R  =  N h2 / (4 π2 K e2 m)  =  N * 5.29e-11 meters
Electron energy    =  E  =  - .5 K e2 / (R N2)    =  N-2 2.18e-18 Joules  =  N-2 13.6 electron Volts          (Ionization energy)

For an electron on a circular orbit,

Fe = Fc

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Wavefunctions

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Shells

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Electronegativity

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Main page

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© Jason Maron, all rights reserved.