Part A Calculate the wavelengths of the first four members of the Paschen series

Question

Part A
Calculate the wavelengths of the first four members of the Paschen series in the spectrum of hydrogen.
answer is The first four members are 1876 nm; 1282 nm; 1094 nm; and 1005 nm

Part B
What is the series limit for the Paschen series?
Part C
Light from a hydrogen discharge passes through a diffraction grating and registers on a detector 1.5 m behind the grating. The m=1 diffraction of the first member of the Paschen series is located 60.7 cm from the central maximum. What is the position of the second member of the Paschen series

Explanation / Answer

1/lambda = (Rydberg constant) * [(1/3)^2 - (1/n)^2] Rydberg constant = 1.097x10^7m^-1 = 1.097x10^-2nm^-1 so... lambda(n=4) = 1/[1.097x10^-2nm^-1 * (1/9 - 1/16)] = 1875nm an so on for n=5 and n=6: n=5 --> 1282nm n=6 --> 1094nm n=7-->1005nm for series limit substtute n = infinity u get lambda(n=infinity) = 1/[1.097x10^-2nm^-1 * (1/9 - 0)] =820.41nm distance is directly proportiona to waveength hence position of second member = 60.7/1876*1282 = 41.48cm

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