Answer :

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

E_{4}-E_{1} = hν

Where h = Planck’s constant

ν = frequency of the photon absorbed.

Therefore, we can write

∴ the frequency of absorbed photon is 3.1× 10^{15} Hz.

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