Question

An electron in a hydrogen-like atom in the n = 3 orbital has a de Broglie wavelength of 1.89x10-10 m.

Calculate the orbit radius of the electron, in nm.

Answer 1

According to de Broglie, electron revoloving around nucleus can be considered as a wave.

Only those wavelength which forms a standing waves will be allowed.

Condition for standing wave is that it should have nodes at the end point.

Total length of the orbit = circumference of the orbit

For an electron revolving in the nth orbit, condition for standing wave