A line in the Paschen series of hydrogen has a wavelength of 1010nm. From what state did the electron originate?

N1=3 (always)

wavelength=1010/10^9 m=1.01/10^6 m (converted into metre)

n2=?

we have a formula

1/wavelength = 1.09677x10^7[ (1/n1^2) - (1/n2^2) ]

10^6/1.01 = 1.01677x10^7[1/9-1/n2^2]

(9.174x10^5) / (1.09677x10^7) = 1/9-1/n2^2

0.08365=0.1111-1/n2^2

1/n2^2=0.1111-0.08365

n2^2=1/0.02746

n2=6

means this electon's ground (original) state was n1=3. After gaining energy it went to n2=6 and when it came back to n1=3, it removed that energy which was seen in the form of spectral lines and these lines had a wavelength of 1010nm.

the lines are observed in infrared region of the electromagnetic spectrum.