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Light of wavelength 12818Ã… is emitted w...

Light of wavelength 12818Ã… is emitted when the electron of a hydrogen atom drops from 5th to 3rd orbit. Find the wavelength of the photon emitted when the electron falls from 3rd to 2nd orbit.

Text Solution

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We know that,
`(1)/(lamda)=R[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))]`
When `n_(1)=3 and n_(2)=5`
`(1)/(12818)=R[(1)/(9)-(1)/(25)]=(16R)/(9xx25)`
or `12818=(9xx25)/(16xxR)` . . .(i)
When `n_(1)=2 and n_(2)=3`
`(1)/(lamda)=R[(1)/(4)-(1)/(9)]=(5R)/(36)` . . . (i)
`lamda=(36)/(5R)`.
dividing (ii) by eqn. (i),
`(lamda)/(12818)=(36)/(5R)xx(16R)/(9xx25)=(64)/(125)`
`lamda=(64)/(125)xx12818=6562.8` Ã…
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