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Q 12.3 What is the shortest wavelength present in the Paschen series of spectral lines?

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The Rydberg's formula for the hydrogen atom is

\frac{1}{\lambda }=R\left [ \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right ]

Where R is Rydberg constant for the Hydrogen atom and equals to 1.1\times107 m-1

For shortest wavelength in Paschen Series n1=2 and n2=\infty

\frac{1}{\lambda }=1.1\times 10^{7}\left [ \frac{1}{3^{2}}-\frac{1}{\infty^{2}} \right ]

\lambda =8.18\times 10^{-7}\ m

The shortest wavelength in Paschen Series is therefore 818 nm.

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Sayak

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