We have seen the Thomson Model and the reasons for its failure. To continue with the chronological scheme of things, I will give here some more insight on the Rutherford Model of the atom that followed the rejection of the Plum-Pudding Model.
We have heard quite a bit about the Rutherford Model of a dense positively charged nucleus surrounded by particle-like electrons that revolve around it like a system of planets under a gravitational field. We have also read about the fact that given such a crude model, the electron will inevitably collapse into the nucleus.
Let's see why.
Consider a stationary charge. Now let the charge experience a sudden acceleration which causes it to move in a particular direction. Initially, the electric field lines from the charge emanate as they should, from a stationary particle. Once the charge is accelerated, distant observers must be able to get the news of this surge, not instantly, but at the speed of information transfer(the speed of light). To enable this, the charge sends out a transverse field line, which travels at the speed of light. This, hence gives rise to the perpendicular component of the electric field which is 1/r dependent.
This phenomenon is responsible for the Larmor formula for radiation. In essence, the information transfer that accompanies the acceleration of the charge causes it to lose energy. As the particle moves, it radiates energy (in the form of electromagnetic radiation, due to the transverse field lines) as:
)
Integrating both sides with respect to the radius, we get the time when the particle falls into the nucleus as:
We have heard quite a bit about the Rutherford Model of a dense positively charged nucleus surrounded by particle-like electrons that revolve around it like a system of planets under a gravitational field. We have also read about the fact that given such a crude model, the electron will inevitably collapse into the nucleus.
Let's see why.
Consider a stationary charge. Now let the charge experience a sudden acceleration which causes it to move in a particular direction. Initially, the electric field lines from the charge emanate as they should, from a stationary particle. Once the charge is accelerated, distant observers must be able to get the news of this surge, not instantly, but at the speed of information transfer(the speed of light). To enable this, the charge sends out a transverse field line, which travels at the speed of light. This, hence gives rise to the perpendicular component of the electric field which is 1/r dependent.
This phenomenon is responsible for the Larmor formula for radiation. In essence, the information transfer that accompanies the acceleration of the charge causes it to lose energy. As the particle moves, it radiates energy (in the form of electromagnetic radiation, due to the transverse field lines) as:
Now what do we do with this?
We know that the total energy of a particle of charge q, revolving around a central nucleus is:
Substituting this value of energy in the Larmor equation and solving for the time rate of change of radius of the particle, we get:
(This equation was obtained by taking 'a' as the centripetal acceleration =
)
Integrating both sides with respect to the radius, we get the time when the particle falls into the nucleus as:
Putting in the values of final radius as 1 fm and initial radius as 1 angstrom, we get the time taken to fall to be around ten-billionth of a second.
Well that number is way smaller than the average lifetime of most of the atoms we see around us. Hence, the Rutherfordian Model, though elegant and intuitive, is not quite so much correct.
But that wasn't the end of the problems for physicists back then. As we know now, the puzzling question of the dual nature of light kept popping up, with the photoelectric effect and the ground-breaking Young's double slit experiment, each standing testament to one side of the case.
This was the right time for a new model of thinking, and as usual, physics didn't disappoint.
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