Question

State Bohr's postulate to define stable orbits in the hydrogen atom. How does de Broglie's hypothesis explain the stability of these orbits?

Answer 1

According to Bohr, electrons revolve around the nucleus only in those discrete orbits which are non-radiating and for which the angular momentum of the revolving electron is an integral multiple of `h/(2pi)`. These discrete orbits are known as stationary or stable orbits

According to de Broglie, a stationary orbit is that which contains an integral number of de Broglie waves associated with the revolving electron.

For an electron revolving in nth circular orbit of radius r_n,

Total distance covered = circumference of the orbit = `2pir_n`

Therefore, for the permissible orbit, `2pir_n= nlambda`

According to de Broglie, `lambda = h/(mv_n)`

where v_n is the speed of electron revolving in nth orbit.

Therefore

`2pir_n = (nh)/(mv_n)`

or

`mv_nr_n = (nh)/(2pi)  = n(h/(2pi))`

Thus, angular momentum of electron revolving in nth orbit must be an integral multiple of  `h/(2pi)` which is same as proposed by bohr's  second postulate defining stable orbits.