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Chapter 6: Problem 102

Show that the entire Paschen series lies in the infrared part of the spectrum.

Short Answer

Expert verified
The entire Paschen series lies in the infrared part of spectrum as the calculated wavelengths for various transitions fall into the range of infrared region (700 nm to 1 mm).

Step by step solution

01

Understanding the Paschen series

The Paschen series is a set of transition lines in the atomic spectrum of hydrogen when the electron makes a transition to the n=3 energy level from any level greater than 3. The wavelength (λ) of the emitted light can be determined by the formula: \(λ = \frac{{R_H}}{{\frac{1}{m²} - \frac{1}{n²}}}}\) where \(R_H\) is the Rydberg constant for hydrogen, \(m\) is the energy level where the electron drops from, and \(n\) is the energy level where the electron drops to which is 3 in the Paschen series.
02

Determining the limits of the Paschen series

For a Paschen series, as the electron transitions to the 3rd energy level, the minimum value for \(m\) is 4 (since \(m\) must be greater than \(n\)). The maximum value for \(m\) is infinite (electron could be outermost before transitioning). When \(m = 4\), the maximum frequency of Paschen series is obtained and conversely, when \(m = ∞\), the minimum frequency is obtained. Use these limits to calculate the maximum and minimum wavelength.
03

Calculating the maximum and minimum wavelength

Calculate the maximum and minimum wavelength using the formula \(λ = \frac{{R_H}}{{\frac{1}{m²} - \frac{1}{n²}}}}\) with the given values of \(m\) and \(n\).
04

Conclusion

The calculated wavelengths lie in the infrared region of the spectrum as the range of the infrared region is from approximately 700 nm to 1 mm. Thus, it can be concluded that the entire Paschen series lies in the infrared part of the spectrum.

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