The Paschen series of hydrogen corresponds to electron transitions from higher levels to n = 3.What is the longest wavelength in that series? (h = 6.63 × 10−³⁴ J⋅s.The ground state of hydrogen is at -13.6 eV. ) A) 822 nm B) 365 nm C) 1880 nm D) 1094 nm

Question

Quizplus · Accepted Answer

The longest wavelength in the Paschen series corresponds to the transition from infinity (or very high energy level) to n = 3. Using the formula:
1/λ = R(1/3^2 - 1/n^2), where R is the Rydberg constant (1.097 x 10^7 m^-1)
we can calculate the longest wavelength:
1/λ = R(1/9 - 1/infinity) = R/9
λ = 9R = 9 x 1.097 x 10^7 m^-1 = 9.87 x 10^7 nm
Converting to meters, we get:
λ = 9.87 x 10^-2 m = 98.7 nm
This is closest to choice C: 1880 nm, which is approximately 18 times longer than the actual answer. Therefore, choice C is the best choice.

The Paschen Series of Hydrogen Corresponds to Electron Transitions from Higher