Question

Hydrogen exhibits several series of line spectra in different spectral regions. For example the Lyman series (nf = 1 in Balmer-Rydberg equation) occurs in the ultraviolet region while the Balmer (nf = 2) series occurs in the visible range and the Paschen (nf = 3), Brackett (nf = 4) and Pfund ( nf = 5) series all occur in the infrared range. What is the shortest-wavelength (in nm) in the Brackett series?

Answer 1

shortest wavelength will be when energy difference is largest

so, nf = 4 and ni must be infinity

1/wavelength = R* (1/nf^2 - 1/ni^2)

R is Rydberg constant. R = 1.097*10^7

1/wavelength = R* (1/nf^2 - 1/ni^2)

1/wavelength = 1.097*10^7* (1/4^2 - 1/inf^2)

1/wavelength = 1.097*10^7* (1/4^2 - 0)

wavelength = 1.459*10^-6 m

wavelength = 1459 nm

Answer: wavelength = 1459 nm