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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.

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Solution

A) Bohr's Postulates
1. An atom has a number of stable orbits in which an electron can reside without the emission of radiant energy. Each orbit corresponds, to a certain energy level.
2. An electron may jump spontaneously from one orbit (energy level E1) to the other orbit (energy level E2)(E2>E1); then the energy change AE in the electron jump is given by Planck's equation
ΔE=E2E1=hv
3. The motion of an electron in a circular orbit is restricted in such a manner that its angular momentum is an integral multiple of h2π
4. A special surface around the nucleus which contained orbits of equal energy and radius was called the shell. These shells are numbered from inside to outwards as 1, 2, 3, 4 etc. and called K, L, M, N respectively.

B. 1λ=RH[112142]
λ=1615RH
Frequency=cλ
so f=2.8×1015Hz



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