A hydrogen atom, initially at rest in the n = 3 quantum state, undergoes a transition to the ground state, emitting a photon in the process. What is the speed of the recoiling hydrogen atom?

Explanation

To solve the problem of finding the speed of the recoiling hydrogen atom after it transitions from the n = 3 state to the ground state (n = 1) while emitting a photon, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Transition**:
The hydrogen atom transitions from the n = 3 state to the n = 1 state. This transition will emit a photon.

2. **Calculate the Wavelength of the Emitted Photon**:
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