Find the ratio between the wavelength of the most energetic' spectral lines in the Balmer and Paschen series of the hydrogen spectrum.

Explanation

To find the ratio between the wavelengths of the most energetic spectral lines in the Balmer and Paschen series of the hydrogen spectrum, we will follow these steps:

### Step 1: Understand the Series
The spectral lines of hydrogen are categorized into different series based on the principal quantum numbers involved in the electron transitions. The Balmer series corresponds to transitions where the electron falls to the second energy level (n1 = 2), while the Paschen series corresponds to transitions where the electron falls to the third energy level (n1 = 3).

### Step 2: Identify the Most Energetic Lines
The most energetic spectral line in any series corresponds to the transition from the highest energy level (n2 = ∞) to the lowest energy level (n1).
- For the Balmer series, the transition is from n2 = ∞ to n1 = 2.
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