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

explanation: it gains negative electrons, therefore becoming negatively charged. as charge cannot be created, nor destroyed, only transferred, this leaves the wool positive. now that they have opposite charges, the two items attract.