The longest wavelength associated with Paschen series is : (Given RH =1.097 × 10^7 SI unit)

Question

The longest wavelength associated with Paschen series is : (Given \(\mathrm{R}_{\mathrm{H}}=1.097 \times 10^{7}\ \mathrm{SI}\) unit)

(1) \(1.094 \times 10^{-6} \mathrm{m}\)

(2) \(2.973 \times 10^{-6} \mathrm{m}\)

(3) \(3.646 \times 10^{-6} \mathrm{m}\)

(4) \(1.876 \times 10^{-6} \mathrm{m}\)   

Answer 1

Correct option is : (4) \(1.876 \times 10^{-6} \mathrm{m}\)   

For longest wavelength in Paschen's series:

\(\frac{1}{\lambda}=\mathrm{R}\left[\frac{1}{\mathrm{n}_{1}{ }^{2}}-\frac{1}{\mathrm{n}_{2}{ }^{2}}\right]\)

For longest n₁ = 3

n₂ = 4

\(\frac{1}{\lambda}=\mathrm{R}\left[\frac{1}{(3)^{2}}-\frac{1}{(4)^{2}}\right]\)

\(\frac{1}{\lambda}=\mathrm{R}\left[\frac{1}{9}-\frac{1}{16}\right]\)

\(\frac{1}{\lambda}=\mathrm{R}\left[\frac{16-9}{16 \times 9}\right]\)

\(\Rightarrow \lambda=\frac{16 \times 9}{7 \mathrm{R}}=\frac{16 \times 9}{7 \times 1.097 \times 10^{7}}\)

\(\lambda=1.876 \times 10^{-6} \mathrm{~m}\)