A photon emitted during the de-excitation of electron from a staten to the first excited state in a hydrogen atom, irradiates a metallic cathode of work function 2 eV, in a photo cell, with a stopping potential of 0.55 V. Obtain the value of the quantum number of the state n.

Explanation

To solve the problem, we need to follow these steps:

### Step 1: Understand the problem
We are given a photon emitted during the de-excitation of an electron in a hydrogen atom from a state \( n \) to the first excited state (\( n_1 = 2 \)). The photon irradiates a metallic cathode with a work function of 2 eV and a stopping potential of 0.55 V. We need to find the quantum number \( n \).

### Step 2: Use the photoelectric effect equation
The energy of the photon can be expressed as:
\[
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