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  4. If the shortest wavelength in Lyman series of hydrogen atom is A, then the longest wavelength in Paschen series of He+ is :

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Q. If the shortest wavelength in Lyman series of hydrogen atom is $A$, then the longest wavelength in Paschen series of $He^{+}$ is :

JEE MainJEE Main 2017Structure of Atom

Solution:

Shortest wavelength is corresponding to best ine
nL = 1 (Lyman series)
nH = $\infty$ (infinite)
$\frac{1}{A}=r\times\left(1\right)^{2}\left\{\frac{1}{12}-\frac{1}{2}\right\}=R$
Longest wavelength = 1st Line
= 3 nH = 4
$\frac{1}{\lambda}=r\times\left(2\right)^{2}\left\{\frac{1}{3^{2}}-\frac{1}{4^{2}}\right\}=\frac{r\times7}{36}$
$\lambda=\frac{36A}{7}$