Question

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

Answer 1

Statement of Bohr's postulate

Explanation in terms of de Broglie hypothesis

 Bohr's postulate, for stable orbits, states

“The electron, in an atom, revolves around the nucleus only in those orbits for which its angular momentum is an integral multiple of h/2π (h = Planck's constant),”

[Also accept mvr = n h/2π (n =1,2,3,…….)

As per de Broglie's hypothesis λ = h/p h/mv

For a stable orbit, we must have circumference of the orbit = n λ (n =1,2,3,…….)

2πr = n.mv 

 or mvr = nh/2π

Thus de –Broglie showed that formation of stationary pattern for integral 'n' gives rise to stability of the atom. This is nothing but the Bohr's postulate.

Detailed Answer :

 According to Bohr’s postulate of Quantisation condition, electrons can revolve only in those orbits in which its 

angular momentum L = mvr is an integral multiple of  h/2π i.e.

  So, circumference of n^th stable orbit for electron can contain exactly n wavelength of de–Broglie (i. e. λ=h/p) associated with the electron in that orbit.