Question

Explain Bohr's stable orbit.

Hint:

Bohr's stable orbit = Electron's angular momentum is quantized and it does not emit radiation in these orbits.

Answer 1

Bohr's stable orbit refers to the concept proposed by Niels Bohr in 1913 to explain the stability of electrons in atoms. According to classical electromagnetism, electrons should spiral into the nucleus due to radiation of energy as they accelerate in orbit. However, Bohr introduced the idea of quantized orbits to solve this problem. The key points of Bohr's theory of stable orbits are:
1. Quantization of Angular Momentum: Bohr proposed that electrons in an atom can only occupy certain discrete orbits around the nucleus. The electron's angular momentum (\(L\)) in these orbits is quantized and must satisfy the condition: \[ L = n \hbar \] Where \(n\) is a positive integer (the principal quantum number), and \(\hbar\) is the reduced Planck's constant. This quantization of angular momentum prevents the electron from spiraling into the nucleus.
2. No Radiation in Stable Orbits: According to Bohr's model, electrons in stable orbits do not emit radiation, despite being accelerated in circular motion. This was a significant departure from classical electrodynamics, where moving charged particles emit radiation. The electron only emits radiation when it transitions from one orbit to another, leading to the emission or absorption of specific energy levels corresponding to the difference between orbits.
Thus, Bohr's stable orbits are those in which the electron has quantized angular momentum, and it remains stable without emitting radiation. These orbits explain the discrete spectral lines observed in atomic spectra.