Final answer:
The value of n_high for the Paschen series line with a wavelength of 1094.4 nm in the hydrogen spectrum is 6, corresponding to the transition starting from the 6th energy level to the 3rd energy level.
Step-by-step explanation:
The wavelength of a certain line in the Paschen series of the hydrogen atom is given as 1094.4 nm. The Paschen series corresponds to electronic transitions that end at the n=3 energy level. Applying the Rydberg formula for the Paschen series:
Rydberg formula: 1/λ = R (1/nf^2 - 1/ni^2), where λ is the wavelength, R is the Rydberg constant (1.097 x 10^7 m^-1), nf is the final energy level (constant at 3 for Paschen), and ni is the initial energy level.
Plugging the values into the formula and solving for ni:
1/1094.4 nm = 1.097 x 10^7 m^-1 (1/3^2 - 1/ni^2)
Solving for ni gives us the value of n_high, which for this specific transition, is 6. Therefore, the correct answer is (c) 6.