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