A beam of electrons bombards a sample of hydrogen. Through what potential difference must the electron have been accelerated if the first line of the Balmer series is to be emitted?

Explanation

To find the potential difference through which electrons must be accelerated to emit the first line of the Balmer series in hydrogen, we can follow these steps:

### Step 1: Identify the Quantum States
The first line of the Balmer series corresponds to the transition from \( n_2 = 3 \) to \( n_1 = 2 \).

### Step 2: Use the Rydberg Formula
The Rydberg formula for the wavelength (\( \lambda \)) of the emitted photon is given by:
\[
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