Question

Show that Bohr’s second postulate ‘the electron revolves around the nucleus only in certain fixed orbits without radiating energy can be explained on the basis of de-Broglie hypothesis of wave nature of electron.

Answer 1

According to de-Broglie hypothesis, the wavelength of the wave associated with electron while moving with velocity v is given by

λ = \(\frac{h}{mv}\) .........(i)

According to de-Broglie, stationary orbit is that orbit whose circumference is integral multiple of wavelength of wave associated with electron on that orbit.

If λ is the de-Broglie wavelength of electron while revolving in an orbit of radius r, then

2 πr = nλ 

or λ = \(\frac{2\pi r}{n}\) ............(ii)

From (i) and (ii),

\(\frac{2\pi r }{n} = \frac{h}{mv}\) 

or mvr = \( \frac{nh}{2\pi}\)

i.e. Total angular momentum = n \((\frac{h}{2\pi})\)

This is stated by Bohr about his stationary orbits.