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Question:

Using Bohr's second postulate of quantization of orbital angular momentum, show that the circumference of the electron in the nth orbital state in a hydrogen atom is n times the de-Broglie wavelength associated with it. The electron in a hydrogen atom is initially in the third excited state. What is the maximum number of spectral lines which can be emitted when it finally moves to the ground state?

Solution:

(A) Postulate of quantization of orbital angular momentum states
mvr = nh/2π
=> 2πr = nh/mv
The left hand side is the circumference of the electron in nth orbital, and right hand side is n times the wavelength associated with atom in nth state (h/mv)
(B) 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