Question

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

(b) A hydrogen atom initially in the ground state absorbs a photon which excites it to the n = 4 level. Estimate the frequency of the photon.

Answer 1

(a) According to Bohr postulate, the electron can revolve around the nucleus in those orbits for which the orbital angular momentum is integral multiple of h/2π. These orbits are called non-radiating or stationary orbits.

Bohr suggested that stationary orbits are those in which orbital circumference (2πr) is an integral multiple of de-Broglie wavelength λ i.e., stationary orbits for an electron are those which contain the complete waves of electron. So we have

2πr = nλ,

where n = 1, 2, 3, ...........(ii)

Also λ = \(\frac{h}{mv}\)

∴ 2πr = n\(\frac{h}{mv}\)

or m v r = \(\frac{h}{2\pi}\) .............(iii)

mvr is the angular momentum of the electron as particle. The equation (iii) corresponds to the Bohr's 2nd postulate, i.e, the total angular momentum of the moving electron is an integral multiple of ω. So the new concept of de-Broglie confirms Bohr's postulate.

(b) Given n₁ = 1 and n₂ = 4