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(i) State Bohr's quantization conditi...

(i) State Bohr's quantization condition for defining stationary orbits . How does de- Broglie hypothesis explain the stationary orbits ?
(ii) find the relation beween the three wavelengths
`lambda_(1), lambda _(2) " and " lambda_(3)` from the energy level diagram shown :

Text Solution

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Only those orbits are stable for which the angular momentum of revolving electron is an integral multiple of `(h/(2pi))` where h is the planck’s constant. Thus the angular momentum (L) of the orbiting electron is quantised. That is `L = (nh)/(2pi)`
According to dc Broglie hypothesis
Linear momentum `= h /lamda`
and for circular orbit
L = rnp, where rn is the radius of quantised
orbits
`=r_nh/lamda`
Also, `L=(nh)/(2pi)`
`:. (r_nh)/lamda=(nh)/(2pi) " or " 2pir=nlamda`
Hence, circumference of permitted orbits are integral multiples of the wavelength
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