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Electron in a sample of H- atoms make tr...

Electron in a sample of `H-` atoms make transitions from state `n=x` to some lower excited state. The emission spectrum from the sample is found to contain only the lines belonging to a particular series. If one of the photons had an energy of `0.6375 eV`. Then find the value of `x. [" Take " 0.6375eV=(3)/(4)xx0.85eV]`.

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The correct Answer is:
x=8
We have
`DeltaE=3/4xx0.85eV`
as energy=0.6375 the photon will belong to brackett series (as for brackett`0.31leEle0.85`)
`0.85xx(1-1/4)=13.6(1/4^2-1/n^2)`
`0.85(1-1/4)=13.6/16[1/(4/n)^2] :. 4/n=1/2 implies n=8` Hence x=8
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