What is the ratio of minimum to maximum wavelength in the Balmer series?

Explanation

The explanation is given below: The Balmer series in the hydrogen atom's emission spectrum has different lines with varying wavelengths. To find the ratio of the shortest (minimum) wavelength to the longest (maximum) wavelength in this series, we consider the two extreme cases. The minimum wavelength occurs when the electron transition is from the third energy level (n = 3) to the second energy level (n = 2). The maximum wavelength happens when the electron transition approaches infinity, which is effectively like taking the limit as n becomes very large. The ratio of the maximum to minimum wavelength is 9:5. In simpler terms, the maximum wavelength is 9/5 times longer than the minimum wavelength in the Balmer series.