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  4. What is the lowest energy of the spectral line emitted by the hydrogen atom in the Lyman series?

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Q. What is the lowest energy of the spectral line emitted by the hydrogen atom in the Lyman series?

Structure of Atom

Solution:

We know that

$\Delta E = hcR _{ H }\left(\frac{1}{ n _{1}^{2}}-\frac{1}{ n _{2}^{2}}\right)$

For the lowest energy of spectral line in the lyman series

$n _{1}=1, n _{2}=2$

Hence, $\Delta E = hc R _{ H }\left(\frac{1}{(1)^{2}}-\frac{1}{(2)^{2}}\right)$

$= hcR _{ H }\left(\frac{1}{1}-\frac{1}{4}\right)$

$=\frac{3 hcR _{ H }}{4}$