Classical nature of the hydrogen atom

[yomister123]

Homework Statement

According to the classical nature of the hydrogen atom an electron in a circular orbit of radius 5.3*10^-11m around a proton fixed at the centre is unstable. If it is true, how long would it take for the electron to collaspse into the proton?

Homework Equations

There is a hint: "Use integral calculus to solve the classical expression for radiation from an accelerated charge"

The Attempt at a Solution

I really don't know where to start... can anyone care to tell me what is the "classical expression for radiation"?

 

[yomister123]

can anyone suggest where to start?

 

[m2003]

I can provide some insight into this question. The classical nature of the hydrogen atom refers to the model proposed by Niels Bohr in 1913, which states that the electron orbits the nucleus in a circular path, similar to the motion of planets around the sun. This model was later refined by Erwin Schrödinger, who introduced the concept of wave functions to describe the electron's behavior.

In this model, the electron is constantly accelerating towards the nucleus due to the attractive force of the positively charged proton. According to classical physics, an accelerated charged particle will emit electromagnetic radiation. This is known as the "classical expression for radiation" and can be described by the Larmor formula, which calculates the power radiated by an accelerated charge.

Using this formula, we can estimate the time it would take for the electron to collapse into the proton. However, it is important to note that this classical model is not entirely accurate and has been replaced by the quantum mechanical model, which describes the electron's behavior as a probability distribution rather than a fixed orbit.

In summary, the classical nature of the hydrogen atom does predict the instability of the electron's orbit, but the exact time it would take for the electron to collapse cannot be accurately determined using classical physics. It is important to consider the limitations of this model and the advancements made in our understanding of atomic structure through quantum mechanics.