In 1911, New Zealand physicist Ernest Rutherford, along with his collaborators, carried out an experiment in which he bombarded a very thin gold blade with alpha particles from polonium (radioactive chemical element), the analysis of this experiment allowed Rutherford to reach conclusions that culminated in the announcement of a new atomic model, in which he assumed that the atom was composed of a dense, positive nucleus, with electrons orbiting in your return.
However, classical physics harshly criticized Rutherford's model, because according to Maxwell's classical electromagnetism, an accelerated-moving charge emits electromagnetic waves, so an electron rotating around the nucleus should emit radiation, losing energy and eventually falling into the nucleus, and we already know that it doesn't it happens.
In 1914, Danish physicist Niels Bohr proposed a model that came to be known as the Bohr atom, or Bohr atomic model, based on postulates that would solve the problems of the Rutherford model, explaining why the electrons would not spirally fall into the core. As he was predicting classical physics, Bohr assumed that electrons revolved around the nucleus in orbits. possible, defined and circular due to the electrical force, which can be calculated by Coulomb's Law through of the equation:
F = ke²
r²
He called them stationary orbits, besides, electrons don't spontaneously emit energy, to jump from one orbit to another it needs to receive an energy photon that can be calculated thus:
E = Ef - ANDi = hf
That way, unless it receives exactly the amount of energy needed to jump from one orbit to another, farther away from the nucleus, the electron will remain in its orbit indefinitely.
The energy corresponding to each orbit was calculated by Bohr, see how we can reach the same result:
The electric force acts as a centripetal force, so we have:
mv² = ke², then mv² = ke² (I)
r r² r
The kinetic energy of the electron is given by Eç = ½ mv². Where do we get that:
ANDç = ke²
2nd
The potential energy of the electron is given by: EP = - ke² (II)
r
The total energy will be: E = Eç + ANDP
E = ke² – ke² = - ke² (III)
2r r 2r
Niels Bohr further assumed that the product mvr should be an integer multiple (n) of h/2π, that is:
mvr = huh
2π
with n = 1,2,3...
So we can do:
v = huh (IV)
2πmr
Substituting this value in equation (I) we have:
m( huh )² = ke²
2πmr r
mn²h² = ke²
4π²m²r² r
which results in: n²h² = ke²
4π²mr² r
n²h² = ke²
4π²mr
4π²mr = 1
n²h² ke²
Therefore r = n²h²
4π²mke²
r = h² . n² (V)
4π²mke²
Replacing V in III
ANDno = - 2π² m k²e4 . 1 (SAW)
h² n²
With equation (VI) above, it is possible to calculate the energy of the electron in the allowed orbits, where n = 1 corresponding to the lowest state energy, or ground state, which it will leave only if it is excited through a received photon, jumping to a more energy, in which it will remain for an extremely short period of time, soon it will return to the ground state emitting a photon of energy. Bohr's atomic model explained the monoelectronic atom of hydrogen well, and for more atoms complexes, a new theory would still be needed, the Schroedinger theory, which is already in the domains of mechanics. quantum.
By Paulo Silva
Graduated in Physics
