You measure the emission spectrum of an atom that you suspect to be hydrogen. you have no absolute calibration of the wavelength, but the ratios of the first 3 wavelengths in the series that you measure are 1 : 0.741 : 0.661. which series is this (e. g. lyman, balmer, paschen, brackett)? justify your answer.

Explanation:

What we need to do here is to determine the ratios by using  the Rydberg equation starting with the transition to n1 = 1, 2,3, etc and see which one fits the data. Remember the question states that they are series and the wavelengths will be for increasing  energy levels.

1/λ = Rh x ( 1/n₁² - 1/n₂²)

Lyman series  ( n₁=1 and n₂= 2,3 etc)  for the first two lines, the ratios will be:

1/λ₁ /1/λ₂  =(1/1 -1/ 2²) / (1/1 -1/ 3²) ⇒ 0.84 ≠ 0.74  (the first ratio)

For Balmer series n₁ = 2  and n₂ = 3,4,5, etc

1/λ₁ /1/λ₂  =(1/4 -1/3²) / (1/4 -1/4²) ⇒ 0.741 = 0.741 (match!)

Lets use the third line to check our

1/λ₁ /1/λ₂  =(1/4 -1/3²) / (1/4 -1/5²) = 0.66

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