(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.
a) 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” , where h = Planck’s constant.
De Broglie wavelength of a particle is given as
Where λ = wavelength of the moving particle
h = Planck’s constant = 6.63× 10-34 Js
p = momentum of moving particle
We know that momentum is given as
p = m× v
where m = mass of the particle
v = velocity of the particle
For a stable orbit, we must have circumference of the
orbit = nλ (n = 1,2,3, ... ... . )
Thus de –Broglie showed that formation of stationary pattern for
integral “n‟ gives rise to stability of the atom.
b) We know that for hydrogen atom the energy of nth level is given as
According to question, hydrogen atom is excited from ground state (n = 1) to n = 4 level. So, the energy of photon will be
E4-E1 = hν
Where h = Planck’s constant
ν = frequency of the photon absorbed.
Therefore, we can write
∴ the frequency of absorbed photon is 3.1× 1015 Hz.
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