Question

What is Bohr's quantum condition postulate? How is it explained by de Broglie? What are the shortcomings of Bohr's atomic model? 
 

Hint:

Bohr’s model explains the quantization of energy levels in atoms but fails to explain phenomena involving multiple electron atoms or relativistic effects.

Answer 1

- Bohr's Quantum Condition Postulate: Bohr's quantum condition postulates that the angular momentum \( L \) of an electron revolving in a circular orbit around the nucleus is quantized and is given by: \[ L = n \hbar, \quad n = 1, 2, 3, \dots \] where \( \hbar = \frac{h}{2\pi} \) is the reduced Planck’s constant, and \( n \) is a positive integer known as the quantum number. This postulate leads to the quantization of energy levels in an atom. - Explanation by de Broglie: Louis de Broglie extended Bohr’s model by suggesting that the electron itself exhibits wave-like properties. According to de Broglie, the electron moves as a standing wave, and the wavelength \( \lambda \) of the electron is related to its momentum \( p \) by: \[ \lambda = \frac{h}{p} = \frac{h}{mv}, \] where \( m \) is the mass and \( v \) is the velocity of the electron. In Bohr’s model, the condition for standing waves on an orbit leads to the quantization of angular momentum \( L = n\hbar \), which is in agreement with Bohr’s postulate. - Shortcomings of Bohr's Atomic Model: 1. Bohr's model could not explain the spectra of atoms with more than one electron. 2. It does not account for the fine structure of spectral lines (which arises from relativistic and spin effects). 3. Bohr’s model is inconsistent with the uncertainty principle proposed by Heisenberg, which implies that the position and momentum of an electron cannot both be known precisely. 4. It could not explain the Zeeman effect (splitting of spectral lines in the presence of a magnetic field).