Coulomb

1
Coulombs law
2

• Coulombs law- this law states that the force, F,
  between to charged particles, q1q2, is
  proportional to their charge and the distance, r,
  between them. Charge and force are directly
  proportional, while distance and force are
  inversely proportional. This means as the
  distance increases, the force is decreased by a
  magnitude of the change in the distance squared.
• F-force between two charged particles. This can
  be two negatively charged particles, two
  positively charged particles, or one negative and
  one positive. When the force is a negative value
  it is an attractive force. When it is positive
  it is repulsive.
• K- Coulombs constant 9109Nm2/c2 or 1/4peo,
  eopermittivity of space8.85410-12(c2 /Nm2)
• q1q2- the charges of the particles. They can be
  either negative or positive.
• r- separation of particles

3
Bohrs model using Coulombs law
4
Bohrs model continued

• Rutherfords theory of electrons revolving
  around the nucleus, in various orbits, explains
  why we see a line spectra for hydrogen. However
  this theory did not account for why the electron
  does not collapse into the nucleus. According to
  a classical theory, an accelerated particle
  radiates energy (as electromagnetic
• waves). Thus, an electron in a Rutherford orbit,
  circulating at constant speed but with a
  continually changing direction of its velocity
  vector is being accelerated thus, the electron
  should constantly lose energy by radiating and
  spiral into the nucleus.(hydro re visit)

5
Bohrs continued

• Bohr, however, found a way to explain line
  spectra and why the electron was not spiraling
  into the nucleus. He theorized quantized energy
  levels, and the electrons ability to only move
  between these energy states. Bohrs model states
  that the electron is held into orbit by coulombic
  forces of attraction, between the electron and
  proton of the positively charged nucleus, and the
  centrifugal force of the electron.
• This results in the equations ke2/r2 and mev2/r
  equal to each other, kZe2/r2 mev2/r
• Coulombs law, kq1q2/r2, is rewritten as ke2/r2.
  Where e is the charge of the particle, k is
  Coulombs constant, Z is atomic number, and r is
  the distance the electron is from the nucleus.
• For the centrifugal force equation, mev2/r , me
  is the mass of the electron, v is the velocity of
  the electron, and r is the radius of the
  electrons orbit, around the nucleus.

6
A one electron atom

• In a one electron atom q1q2 are replaced with e2
  and r is now the distance between orbiting
  electron and the nucleus, also known as the
  radius.
• In terms of the equation kZe2/r2 q1q2 are
  replaced with e and Z. Z represents the atomic
  number, or the number of protons in the nucleus.
  This is also the positive charge that pulls the
  electron, e, toward the nucleus. r represents
  the radius of the electrons orbit, or the
  distance between the electron and the proton in
  the nucleus.