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In Li^(++) , electron in first Bohr orbi...

In `Li^(++)` , electron in first Bohr orbit is excited to a level by a radiation of wavelength `lamda` When the ion gets deexcited to the ground state in all possible ways (including intermediate emissions), a total of six spectral lines are observed. What is the value of `lamda` (Given : `h= 6.63 xx 10^(-34) Js, c = 3 xx 10^(8) ms^(-1)`)

Text Solution

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Spectral lines obtained on account of transition from nth orbit to various lower orbits is `(n(n-1))/2`
`implies6=(n(n-1))/2`
`impliesn=4`
`DeltaE=(hc)/(lamda)=(-Z^(2))/(n^(2))(13.6eV)`
`implies1/(lamda)=Z^(2)((13.6eV)/(hc))(1/(n_(2)(2))-1/(n_(1)^(2)))`
`=(13.4)(3)^(2)[1-1/16]eV`
`implieslamda=(1242xx16)/((13.4)xx(9)(15))nm=10.8nm`
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