Answer to Question #216483 in Quantum Mechanics for Qasim Ali

Question

b) State de-Broglie hypothesis. Using de-Broglie hypothesis and one of the Bohr model postulate of the hydrogen atom, show that the wavelength associated with electron revolving around the nucleus is quantized.

Answer 1

According to De Broglie's theory of matter waves, each particle of matter with linear momentum is also a wave. A matter wave's wavelength is inversely related to the magnitude of the particle's linear momentum. They are proof of the existence of matter waves.

The postulate of quantization of orbital angular momentum states

$mvr=\frac{nh}{2π} ⟹2πr=\frac{nh}{mv}$

​The left-hand side is the circumference of the electron in nth

 orbital, and the right-hand side is the n times the wavelength associated with an atom in n^th

 state $(\frac{h}{mv})$

The atom in n=3 could jump back to n=2. After jumping to n=2 it could further jump to n=1.

Hence possible spectrum lines are three corresponding to

$n=3→n=1\\ n=3→n=2\\ n=2→n=1\\$