atomic structure

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Li⁺² ion is hydrogenic and has a Lyman seriies at 740747cm^-1,877924cm^-1,925933cm^-1 and beyond.Show tht the energy levels are of the form -R/n² and find the value of R for this ion. Predict the wave no's of the two longest wavelength transition of the Balmer series of the ion and find the ionisation energy of the ion?

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Lokesh Verma ·2008-11-06 04:31:24

1/Î»₁=R(1/1-1/2²)
1/Î»₁=.75R
1/Î»₂=R(1/1-1/3²)
1/Î»₂=8/9R
1/Î»₃=R(1/1-1/4²)
1/Î»₁=15/16R

Now take the ratios

1/Î»₁:1/Î»₂:1/Î»₃ = 4/3:9/8:16/15

we compare the lamda's above.. the ratio is the same..

so we have shown that the energy levels are as needed!

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Lokesh Verma ·2008-11-06 04:35:27

1/Î»₁=R(1/1-1/2²) = 4/3R

We know Î»₁

so we know R

last part follows simply by taking appropirate n₁ and n₂

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