For gases, the density at boiling point is used. Size data

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/m^{3}Atomic mass unit= M_{0}= 1.661⋅10^{-27}kg Atomic mass = M_{A}= 63.55 Atomic mass units Mass = M = M_{A}⋅M_{0}= 9.785⋅10^{-26}kg Number density = N = D / M = 9.096⋅10^{28}atoms/m^{3}Cube volume = Υ_{cube}= 1 / N = 1.099⋅10^{-29}m^{3}Volume/atom if the atoms are cubes Cube length = L = Υ^{1/3}_{cube}= 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 = Υ_{sph}= Υ_{cube}f = 8.14⋅10^{-30}m^{3}=^{4}⁄_{3}πR^{3}Volume/atom if the atoms are spheres Sphere radius = R = 1.25⋅10^{-10}m

Dot size = Density Color = Shear Modulus, an indicator of the element's strength. Blue: The element is a liquid at room temperature Red: Weak White: StrongShear data Density data

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*10For an electron on a circular orbit,^{-31}kg Electron velocity = V Electron momentum = Q = m V Electron charge = e = -1.60*10^{-19}Coulombs Coulomb constant = K = 9.0*10^{9}Newtons meters^{}/ Coulombs^{2}Electric force = F_{e}= K e^{2}/ R^{2}Centripetal force = F_{c}= M V^{2}/ R Orbit radius = R = N h^{2}/ (4 π^{2}K e^{2}m) = N * 5.29e-11 meters Electron energy = E = - .5 K e^{2}/ (R N^{2}) = N^{-2}2.18e-18 Joules = N^{-2}13.6 electron Volts (Ionization energy)

F_{e}= F_{c}

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