How many different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms excited to states with principal quantum number n?

Explanation

To determine how many different wavelengths may be observed in the spectrum from a hydrogen sample when the atoms are excited to states with principal quantum number \( n \), we can follow these steps:

### Step 1: Understand the transitions
When an electron transitions between energy levels in a hydrogen atom, it emits or absorbs a photon with a specific wavelength. The principal quantum number \( n \) indicates the energy level of the electron.

### Step 2: Identify possible transitions
For an atom excited to the \( n \)th state, the electron can transition to any lower energy level. The possible lower energy levels are \( n-1, n-2, \ldots, 1 \).

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