Prove that Bohr’s condition for quantization of angular momentum in hydrogen atom can be obtained by requiring an integer number of standing waves around an electron orbit. Use de-Broglie wavelength as the wavelength of wave associated with electron.

The de-Broglie wavelength of an electron in the first Bohr orbit is

In the nth orbit of hydrogen atom, find the ratio of the radius of the electron orbit and de-Broglie wavelength associated with it.

What is the de-Broglie wavelength associated with the hydrogen electron in its third orbit

The de broglie wavelength of an electron in the first Bohr orbit is equal to

The de Broglie wavelength of an electron in the 3rd Bohr orbit is

If the kinetic energy of an electron is increased 4 times, the wavelength of the de Broglie wave associated with it would becomes:

Derive Bohr's quantisation condition for angular momentum of orbiting electron in hydrogen atom using De Broglie's hypothesis.

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