A line in the Brackett series of hydrogen has a wavelength of 1945 nm. From what state did the electron originate?

Rydberg Eqn is given as:

1/λ = R [1/n1^2 - 1/n2^2]

Where λ is the wavelength of the light; 2626 nm = 2.626*10^-6 m

R is the Rydberg constant: R = 1.09737*10^7 m-1

From Brackett series n1 = 4

Hence 1 / (2.626*10^-6) = 1.09737 * 10^7 [1/4^2 - 1/n2^2]

Some rearranging and collecting up terms:

1 = (2.626*10^-6) * (1.09737 * 10^7) [1/16 - 1/n2^2]

1 = 28.82[1/16 - 1/n2^2]

28.82/n^2 = 1.8011 - 1 = 0.8011

n^2 = 28.82/0.8011 = 35.98

n = √ (35.98) = 6