Obtain the expression for the ratio of the de Broglie wavelengths associated with the electron orbiting in the second and third excited states of hydrogen atom.

Explanation

To find the ratio of the de Broglie wavelengths associated with the electron in the second and third excited states of a hydrogen atom, we can follow these steps:

### Step 1: Understand the excited states
The second excited state corresponds to the principal quantum number \( n = 3 \) and the third excited state corresponds to \( n = 4 \).

### Step 2: Write the formula for de Broglie wavelength
The de Broglie wavelength \( \lambda \) of an electron in a given orbit can be expressed using the formula:
\[
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