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 can follow these steps:

### Step 1: Understand the Series
The Balmer series corresponds to transitions from higher energy levels to the second energy level (n=2), while the Paschen series corresponds to transitions to the third energy level (n=3). The most energetic spectral line in each series occurs when the electron transitions from an infinitely high energy level (n=∞) to the respective lower energy level.

### Step 2: Write the Formula for Wavelength
The wavelength (λ) of the emitted light can be calculated using the Rydberg formula:
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