How many atoms would be needed to show all the possible transitions from n = 4 to n = 1 in the hydrogen atom?

Explanation

To determine how many hydrogen atoms are needed to show all possible transitions from the energy level \( n = 4 \) to \( n = 1 \), we will analyze the transitions that can occur between these energy levels.

### Step-by-Step Solution:

1. **Identify the Energy Levels**:
The hydrogen atom has discrete energy levels denoted by quantum numbers \( n = 1, 2, 3, \) and \( 4 \). We are interested in transitions starting from \( n = 4 \) and ending at \( n = 1 \).

2. **List Possible Transitions**:
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