(a) How is the stability of hydrogen atom in Bohr model explained by de Broglie's hypothesis?
(b) A hydrogen atom initially in the ground state absorbs a photon which excites it to n = 4 level. When it gets de-excited, find the maximum number of lines which are emitted by the atom. Identify the series to which these lines belong. Which of them has the shortest wavelength?

 

 
 
 
 
 

Answers (1)
S safeer

a) Thus de Broglie hypothesis gives an explanation for Bohr’s second postulate. The quantised electron orbits and energy states are due to the wave nature of the electron and only resonant standing waves can persist.

According to de Broglie hypothesis

2\pi r=n\lambda=\frac{nh}{p}=\frac{nh}{mv}\\\\\Rightarrow mvr=\frac{nh}{2\pi}

b) 6 lines are emitted by the atom, which is during the transition from

1. 4 to 3: Paschen series

2. 4 to 2: Balmer series

3. 4 to 1: Lyman series

4. 3 to 2: Balmer series

5. 3 to 1:  Lyman series

6. 2 to 1:  Lyman series

4 to 1 has the shortest wavelength, which belongs to the Lyman series.

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