# Coulomb`s law and Bohr`s model

```Coulomb’s law
Coulomb’s law- this law states that the force, F, between to charged particles, q1&q2, 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= 9*109N*m2/c2 or 1/4πεo, εo=permittivity of space=8.854*1012(c2 /N*m2)
q1&q2- the charges of the particles. They can be either negative or positive.
r- separation of particles
Bohr’s model using Coulomb’s law
Bohr’s model continued
Rutherford’s theory of electron’s 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)
Bohr’s 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. Bohr’s 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
Coulomb’s law, kq1q2/r2, is rewritten as ke2/r2. Where “e” is the charge of the
particle, k is Coulomb’s 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 electron’s orbit, around the
nucleus.
A one electron atom
In a one electron atom q1&q2 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 q1&q2 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.
```
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