Example 2 Determine the wavelength corresponding to the second spectral line in Paschen series (um)

To determine the wavelength corresponding to the second spectral line in the Paschen series, we need to use the Rydberg formula:<br /><br />1/λ = R * (1/n1^2 - 1/n2^2)<br /><br />where λ is the wavelength, R is the Rydberg constant (1.097373 x 10^7 m^-1), n1 is the lower energy level, and n2 is the higher energy level.<br /><br />For the second spectral line in the Paschen series, n1 = 3 and n2 = 4.<br /><br />Plugging these values into the Rydberg formula:<br /><br />1/λ = R * (1/3^2 - 1/4^2)<br />1/λ = R * (1/9 - 1/16)<br />1/λ = R * (16/144 - 9/144)<br />1/λ = R * (7/144)<br />λ = 144 / (R * 7)<br /><br />Using the value of R = 1.097373 x 10^7 m^-1:<br /><br />λ = 144 / (1.097373 x 10^7 * 7)<br />λ ≈ 1.63 x 10^-6 m<br />λ ≈ 1630 nm<br /><br />Therefore, the wavelength corresponding to the second spectral line in the Paschen series is approximately 1630 nm.