Understanding the Fixed Energy of Electrons in Bohr's Orbit

[harman90]

After Doing lot of research, I still am Unable To Understand,
How a Electron in Fixed orbit (with fixed energy) is not radiating energy as it is continuously accelerating.

According to my Book, Rutherford only missed "Fixed orbit" word in his theory?

Moreover, Speed of electron is described as Velocity, which is constant. how a velocity of a body moving in circular body can be constant?

 

[berkeman]

After Doing lot of research, I still am Unable To Understand,
How a Electron in Fixed orbit (with fixed energy) is not radiating energy as it is continuously accelerating.

According to my Book, Rutherford only missed "Fixed orbit" word in his theory?

Moreover, Speed of electron is described as Velocity, which is constant. how a velocity of a body moving in circular body can be constant?

Welcome to the PF.

Your question is addressed in the 3rd item in the Physics FAQ that is pinned at the top of this General Physics forum:

https://www.physicsforums.com/threads/why-dont-electrons-crash-into-the-nucleus-in-atoms.511179/

Read through that to see if it helps you to better understand the issues.

 

[harman90]

Thank you Very much, well it explains "WHY DON’T ELECTRONS CRASH INTO THE NUCLEUS" which obviously wasnt clear till Bohr,

But my question is HOW bohr atomic theory overcome the Limitation of Rutherfordwhen He actually said the same thing (what Rutherford did) with 3 extra words (fixed energy orbit)

 

[mfb]

Bohr's model did not explain why the electron does not fall into the nucleus. Bohr just assumed that some orbits would be stable, without explanation. Quantum mechanics later gave a reasonable answer.

 

[harman90]

Thank you for the reply. For that to be True, I guess It should have been one of the Biggest Limitation of Bohr Model, Instead All textbooks Mention "bohr model successfully explained the stability of the atom" (which i fail to understand how)

 

[mfb]

It does not "explain" the stability. It gives some good argument why the energy levels could be as they are - in hydrogen and hydrogen-like atoms.

 

[jtbell]

Bohr "explained" the discrete energy levels by assuming that the orbital angular momentum is an integer multiple of $\hbar$: $L = n\hbar$. However, he didn't really explain why this might be true, and it isn't really true anyway: the magnitude of the orbital angular momentum is actually $L = \sqrt{l(l+1)} \hbar$, where l is an integer that can have values of 0,...,n. That is, for a given value of n (energy level), there are usually multiple possible values of l. This can be derived by solving Schrödinger's equation which came along later.

You should not attach any more importance to Bohr's model than that it was the first crude step towards the modern quantum theory of the atom, which took shape about ten years later.