The Paschen series in the Hydrogen emission spectrum is formed by electron transition form ni > 3 to nf = 3. (a) Calculate the longest wavelength in the Paschen series. (b) Calculate the wavelength of the series limit (the lower bound of the wavelength in the series).
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097 \times 10^7 \, \text{m}^{-1} \) is the Rydberg constant, \( n_{\text{i}} = 4 \) and \( n_{\text{f}} = 3 \) for the Paschen series. Show more…
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Use the worked example above to help you solve this problem. The Paschen series for the hydrogen atom corresponds to electronic transitions that terminate in the state with quantum number n = 3. (a) Find the longest-wavelength photon emitted in the Paschen series and determine its frequency and energy. ???? = nm f = Hz E = eV (b) Find the shortest-wavelength photon emitted in the same series. nm
Vishal G.
The Paschen series results from transitions of the electron in hydrogen in which the electron ends at the $\mathrm{n}=3 n=3$ energy level. Using the Rydberg formula for the Paschen series, calculate the wavelengths of the photons emitted in the transitions that end in the $\mathrm{n}=3 n=3$ level and start in the energy levels that correspond to $n$ equal to 4 through 6 and indicate the initial and final levels of the transition corresponding to each wavelength. State whether each wavelength is visible (380 to $750 \mathrm{~nm}$ ), ultraviolet (shorter than $380 \mathrm{~nm}$ ), or infrared (longer than $750 \mathrm{~nm}$ ).
a. Calculate the wavelengths of the first four members of the Paschen series in the spectrum of hydrogen. b. What is the series limit for the Paschen series? c. Light from a hydrogen discharge passes through a diffraction grating and registers on a detector 1.5 m behind the grating. The first-order diffraction of the first member of the Paschen series is located $60.7 \mathrm{cm}$ from the central maximum. What is the position of the second member of the Paschen series?
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