Final answer:
The wavelengths of the first three lines in the Paschen series (ni = 4, 5, and 6) are approximately 1875 nm, 1282 nm, and 1093 nm, respectively.
Step-by-step explanation:
The electrons in hydrogen atoms can jump between different energy levels, emitting light of specific wavelengths in the process. The Paschen series refers to the transitions where the final energy level (nf) is 3 and the initial energy level (ni) is 4, 5, and 6. To calculate the wavelengths, we can use the equation:
wavelength = Balmer constant / (nf^2 - ni^2)
For the first line (ni = 4), the equation gives a wavelength of approximately 1875 nm. For the second line (ni = 5), the wavelength is around 1282 nm. And for the third line (ni = 6), the wavelength is approximately 1093 nm